All India Barc Online Test In Mechanical Engg.

1. Kinamatic Viscosity is Given by

Dynamic Viscosity/ Density

Product of dynamic viscosity and density

Density/dynamic viscosity

Dynamic Viscosity /momentum

The correct answer is dynamic viscosity/ density. This is because kinematic viscosity is defined as the ratio of dynamic viscosity (a measure of a fluid's resistance to flow) to density (the mass per unit volume of a substance). Therefore, dividing dynamic viscosity by density gives us the kinematic viscosity.

Explanation

The correct answer is dynamic viscosity/ density. This is because kinematic viscosity is defined as the ratio of dynamic viscosity (a measure of a fluid's resistance to flow) to density (the mass per unit volume of a substance). Therefore, dividing dynamic viscosity by density gives us the kinematic viscosity.

2. A Tank is initially empty after sometime Water from height h is falling into the tank with Volume flow rate is Q , the Velocity of the water when it hits the Tank surface is 2 m/s at any instant of time the mass of tank and Water is 250 Kg and Accelaration due to gravity is 10 m/sec^2 . Then Total force (N) resisted by the weighing balance at that instant of time is

2500 + 2000 Q

2000 + 2000 Q

2000 + 2500 Q

2500 + 2500 Q

The total force resisted by the weighing balance at that instant of time can be calculated using the equation F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity. In this case, the mass of the tank and water is given as 250 kg. Therefore, the force is equal to 250 kg multiplied by 10 m/s^2 (acceleration due to gravity), which gives us 2500 N. Additionally, the velocity of the water when it hits the tank surface is given as 2 m/s. The force due to the water hitting the tank surface can be calculated using the equation F = mv, where m is the mass and v is the velocity. Therefore, the force due to the water hitting the tank surface is equal to 2000 Q N (Q is the volume flow rate). Therefore, the total force resisted by the weighing balance at that instant of time is 2500 + 2000 Q N.

Explanation

The total force resisted by the weighing balance at that instant of time can be calculated using the equation F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity. In this case, the mass of the tank and water is given as 250 kg. Therefore, the force is equal to 250 kg multiplied by 10 m/s^2 (acceleration due to gravity), which gives us 2500 N. Additionally, the velocity of the water when it hits the tank surface is given as 2 m/s. The force due to the water hitting the tank surface can be calculated using the equation F = mv, where m is the mass and v is the velocity. Therefore, the force due to the water hitting the tank surface is equal to 2000 Q N (Q is the volume flow rate). Therefore, the total force resisted by the weighing balance at that instant of time is 2500 + 2000 Q N.

3. The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is 400 N. The turning was performed using 2 mm depth of cut and 0.1 mm/rev feed rate. The specific cutting pressure (in N/mm2) is

1000

2000

3000

4000

The specific cutting pressure can be calculated using the formula: Specific cutting pressure = Cutting force / (Depth of cut x Feed rate). In this case, the cutting force is given as 400 N, the depth of cut is 2 mm, and the feed rate is 0.1 mm/rev. Plugging in these values, we get: Specific cutting pressure = 400 N / (2 mm x 0.1 mm/rev) = 400 N / (0.2 mm/rev) = 2000 N/mm2. Therefore, the specific cutting pressure is 2000 N/mm2.

Explanation

The specific cutting pressure can be calculated using the formula: Specific cutting pressure = Cutting force / (Depth of cut x Feed rate). In this case, the cutting force is given as 400 N, the depth of cut is 2 mm, and the feed rate is 0.1 mm/rev. Plugging in these values, we get: Specific cutting pressure = 400 N / (2 mm x 0.1 mm/rev) = 400 N / (0.2 mm/rev) = 2000 N/mm2. Therefore, the specific cutting pressure is 2000 N/mm2.

4. A pair of spur gears with module 5 mm and a center distance of 450 mm is used for a speed reduction of 5:1. The number of teeth on pinion is

30

50

60

20

The module of the gears is given as 5 mm, which represents the size of the gear teeth. The center distance between the gears is given as 450 mm. The speed reduction ratio is 5:1, which means the pinion gear (smaller gear) will have 5 times fewer teeth than the larger gear. Therefore, the number of teeth on the pinion gear can be calculated as (number of teeth on larger gear) divided by 5. Since the answer options are 30, 50, 60, and 20, the only option that satisfies this calculation is 30.

Explanation

The module of the gears is given as 5 mm, which represents the size of the gear teeth. The center distance between the gears is given as 450 mm. The speed reduction ratio is 5:1, which means the pinion gear (smaller gear) will have 5 times fewer teeth than the larger gear. Therefore, the number of teeth on the pinion gear can be calculated as (number of teeth on larger gear) divided by 5. Since the answer options are 30, 50, 60, and 20, the only option that satisfies this calculation is 30.

5. Ratio between inertial forces and the square root of pressure forces is known as

Euler number

Weber number

Froude number

Mach number

The ratio between inertial forces and the square root of pressure forces is known as the Euler number. It is a dimensionless number used in fluid dynamics to determine the relative importance of inertial forces compared to pressure forces. The Euler number is commonly used in the study of fluid flow and is named after Swiss mathematician Leonhard Euler.

Explanation

The ratio between inertial forces and the square root of pressure forces is known as the Euler number. It is a dimensionless number used in fluid dynamics to determine the relative importance of inertial forces compared to pressure forces. The Euler number is commonly used in the study of fluid flow and is named after Swiss mathematician Leonhard Euler.

6. A Gas Turbine Cycle with heat exchange and reheating improves

Only the thermal efficiency

Only the Specific power output

Both thermal effiecincy and specific power output

Any one of the above

A Gas Turbine Cycle with heat exchange and reheating improves both thermal efficiency and specific power output. Heat exchange helps in extracting more energy from the fuel, increasing the thermal efficiency of the cycle. Reheating allows for additional expansion of the working fluid, resulting in increased power output. Therefore, both the thermal efficiency and specific power output are improved in a Gas Turbine Cycle with heat exchange and reheating.

Explanation

A Gas Turbine Cycle with heat exchange and reheating improves both thermal efficiency and specific power output. Heat exchange helps in extracting more energy from the fuel, increasing the thermal efficiency of the cycle. Reheating allows for additional expansion of the working fluid, resulting in increased power output. Therefore, both the thermal efficiency and specific power output are improved in a Gas Turbine Cycle with heat exchange and reheating.

7. In Certain type of Heat Exchanger , Both the fluids have identical mass flow rate Specific heat product. The hot fluid enters at 349 K and leaves at 322 K and the cold fluid entering at 301 K leave at 328 K. The effectiveness of HE IS

0.7

0.6

0.2

0.3

The effectiveness of a heat exchanger is a measure of how well it transfers heat from one fluid to another. In this case, both fluids have identical mass flow rate Specific heat product, which means they have the same ability to absorb and release heat. The hot fluid enters at a higher temperature and leaves at a lower temperature, while the cold fluid enters at a lower temperature and leaves at a higher temperature. The effectiveness of 0.6 indicates that the heat exchanger is able to transfer 60% of the available heat from the hot fluid to the cold fluid.

Explanation

The effectiveness of a heat exchanger is a measure of how well it transfers heat from one fluid to another. In this case, both fluids have identical mass flow rate Specific heat product, which means they have the same ability to absorb and release heat. The hot fluid enters at a higher temperature and leaves at a lower temperature, while the cold fluid enters at a lower temperature and leaves at a higher temperature. The effectiveness of 0.6 indicates that the heat exchanger is able to transfer 60% of the available heat from the hot fluid to the cold fluid.

8. Line imperfection in a crystal is called

Schottky defect

Frenkel defect

Edge dislocation

Miller defect

An edge dislocation refers to a line imperfection in a crystal lattice where there is an extra or missing half-plane of atoms. This type of defect causes a distortion in the crystal structure along the line, resulting in localized strain and deformation. Edge dislocations can have significant effects on the mechanical properties of materials, such as increasing their strength and hardness.

Explanation

An edge dislocation refers to a line imperfection in a crystal lattice where there is an extra or missing half-plane of atoms. This type of defect causes a distortion in the crystal structure along the line, resulting in localized strain and deformation. Edge dislocations can have significant effects on the mechanical properties of materials, such as increasing their strength and hardness.

9. In powder metallurgy, the operation carried out to improve the bearing property of a bush is called

Infilteration

Impregnation

Plating

Sintering

Impregnation is the operation carried out in powder metallurgy to improve the bearing property of a bush. Impregnation involves filling the pores of the bush with a lubricant or a solid material to enhance its bearing capacity. This process helps to reduce friction and wear, ensuring smoother operation and longer lifespan of the bush. Infiltration, plating, and sintering are also important operations in powder metallurgy, but they are not specifically aimed at improving the bearing property of a bush.

Explanation

Impregnation is the operation carried out in powder metallurgy to improve the bearing property of a bush. Impregnation involves filling the pores of the bush with a lubricant or a solid material to enhance its bearing capacity. This process helps to reduce friction and wear, ensuring smoother operation and longer lifespan of the bush. Infiltration, plating, and sintering are also important operations in powder metallurgy, but they are not specifically aimed at improving the bearing property of a bush.

10. Wheel loading in grinding is defined as

Types of wheel bond fracture

Types of wheel grain fracture

Sticking of small particle on grinding wheel

None of the above

Wheel loading in grinding is defined as the sticking of small particles on the grinding wheel. During the grinding process, the small particles from the workpiece or the grinding wheel itself can adhere to the surface of the wheel, reducing its cutting ability and causing a decrease in the material removal rate. This phenomenon can lead to poor surface finish, increased heat generation, and shorter wheel life. Therefore, it is important to prevent wheel loading by using appropriate coolant, dressing the wheel regularly, and maintaining proper grinding parameters.

Explanation

Wheel loading in grinding is defined as the sticking of small particles on the grinding wheel. During the grinding process, the small particles from the workpiece or the grinding wheel itself can adhere to the surface of the wheel, reducing its cutting ability and causing a decrease in the material removal rate. This phenomenon can lead to poor surface finish, increased heat generation, and shorter wheel life. Therefore, it is important to prevent wheel loading by using appropriate coolant, dressing the wheel regularly, and maintaining proper grinding parameters.

11. The stress acting on a element in X and Y direction is 40 MPa and 30 Mpa. Then the Average of maximium and minimium Principle Stress is

35

45

50

55

The average of the maximum and minimum principle stress can be calculated by adding the maximum and minimum principle stress values and dividing the sum by 2. In this case, the maximum principle stress is 40 MPa and the minimum principle stress is 30 MPa. Therefore, the average of the maximum and minimum principle stress is (40 + 30) / 2 = 35 MPa.

Explanation

The average of the maximum and minimum principle stress can be calculated by adding the maximum and minimum principle stress values and dividing the sum by 2. In this case, the maximum principle stress is 40 MPa and the minimum principle stress is 30 MPa. Therefore, the average of the maximum and minimum principle stress is (40 + 30) / 2 = 35 MPa.

12. The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is

Normal

Poisson

Erlang

Beta

The Poisson distribution is commonly used to model the number of arrivals of events in a fixed time interval, where the events occur randomly and independently of each other. It is often used in scenarios such as the arrival of customers at a service facility or the occurrence of accidents in a given time period. Therefore, the given probability distribution of the number of arrivals of jobs in a fixed time interval being Poisson is a reasonable and appropriate choice.

Explanation

The Poisson distribution is commonly used to model the number of arrivals of events in a fixed time interval, where the events occur randomly and independently of each other. It is often used in scenarios such as the arrival of customers at a service facility or the occurrence of accidents in a given time period. Therefore, the given probability distribution of the number of arrivals of jobs in a fixed time interval being Poisson is a reasonable and appropriate choice.

13. A Lead Screw with half nuts in a lathe, Free to Rotate in both Direction has

V-threads

Whithworth threads

Buttress threads

ACME threads

ACME threads are the correct answer because they are commonly used in lead screws with half nuts in a lathe. ACME threads have a trapezoidal shape which provides better load-carrying capacity and resistance to wear compared to other thread types. They are designed to allow for smooth and efficient movement in both directions of rotation. V-threads, Whithworth threads, and Buttress threads are not typically used in this specific application.

Explanation

ACME threads are the correct answer because they are commonly used in lead screws with half nuts in a lathe. ACME threads have a trapezoidal shape which provides better load-carrying capacity and resistance to wear compared to other thread types. They are designed to allow for smooth and efficient movement in both directions of rotation. V-threads, Whithworth threads, and Buttress threads are not typically used in this specific application.

14. The enthalpy of steam at the inlet and outlet of a steam turbine is 2850 KJ/Kg and 1950 KJ/Kg respectively. The specifiec steam consumption in Kg/KW hour is

4

3

5

2

not-available-via-ai

Explanation

not-available-via-ai

15. The process of producing components in moulds without the application of pressure, is known as

Moulding

Laminating

Casting

Calendering

Casting is the correct answer because it refers to the process of producing components in moulds without the application of pressure. In casting, a molten material, such as metal or plastic, is poured into a mould and allowed to solidify, forming the desired shape. This process is commonly used in manufacturing industries to create complex and intricate parts with high accuracy and precision. Casting is different from other options like moulding, laminating, and calendering, which involve the application of pressure or other techniques to shape materials.

Explanation

Casting is the correct answer because it refers to the process of producing components in moulds without the application of pressure. In casting, a molten material, such as metal or plastic, is poured into a mould and allowed to solidify, forming the desired shape. This process is commonly used in manufacturing industries to create complex and intricate parts with high accuracy and precision. Casting is different from other options like moulding, laminating, and calendering, which involve the application of pressure or other techniques to shape materials.

16. The damping ratio of a single degree of freedom spring-mass-damper system with mass of 1 kg, stiffness 100 N/m and viscous damping coefficient of 25 Ns/m is

1.25

1.8

1.7

1.9

The damping ratio of a single degree of freedom spring-mass-damper system can be calculated using the formula: damping ratio = damping coefficient / (2 * sqrt(mass * stiffness)). In this case, the damping coefficient is given as 25 Ns/m, the mass is 1 kg, and the stiffness is 100 N/m. Plugging these values into the formula, we get damping ratio = 25 / (2 * sqrt(1 * 100)) = 25 / (2 * 10) = 1.25.

Explanation

The damping ratio of a single degree of freedom spring-mass-damper system can be calculated using the formula: damping ratio = damping coefficient / (2 * sqrt(mass * stiffness)). In this case, the damping coefficient is given as 25 Ns/m, the mass is 1 kg, and the stiffness is 100 N/m. Plugging these values into the formula, we get damping ratio = 25 / (2 * sqrt(1 * 100)) = 25 / (2 * 10) = 1.25.

17. If cohesion between molecules of a fluid is greater than adhesion between fluid and glass, then the free level of fluid in a dipped glass tube will be

Higher than surface of liquid

Same as the surface of liquid

Lower than the surface of liquid

Unpredictable

When the cohesion between molecules of a fluid is greater than the adhesion between the fluid and the glass, the molecules of the fluid tend to stick together more strongly than they stick to the glass. This results in a concave meniscus forming in the dipped glass tube, causing the free level of the fluid to be lower than the surface of the liquid.

Explanation

When the cohesion between molecules of a fluid is greater than the adhesion between the fluid and the glass, the molecules of the fluid tend to stick together more strongly than they stick to the glass. This results in a concave meniscus forming in the dipped glass tube, causing the free level of the fluid to be lower than the surface of the liquid.

18. According to kinectic theory of gases, at absolute zero

Specific heat of molecules reduced to zero

Kinectic energy of molecules reduced to zero

Volume of gas reduce to zero

Pressure of gas reduced to zero

According to the kinetic theory of gases, at absolute zero, the kinetic energy of molecules is reduced to zero. This is because at absolute zero, the temperature of the gas is at its lowest possible value, causing the molecules to have minimal or no motion. As kinetic energy is directly related to the motion of particles, when the motion ceases, the kinetic energy also becomes zero.

Explanation

According to the kinetic theory of gases, at absolute zero, the kinetic energy of molecules is reduced to zero. This is because at absolute zero, the temperature of the gas is at its lowest possible value, causing the molecules to have minimal or no motion. As kinetic energy is directly related to the motion of particles, when the motion ceases, the kinetic energy also becomes zero.

19. A milling cutter having 8 teeth is rotating at 150 rpm. if the feed per tooth is 0.1 mm, the value of thew table speed in mm/min is

120

187

125

70

The table speed is calculated by multiplying the feed per tooth by the number of teeth on the milling cutter and the rotational speed. In this case, the feed per tooth is 0.1 mm, the number of teeth is 8, and the rotational speed is 150 rpm. Multiplying these values together gives a table speed of 120 mm/min.

Explanation

The table speed is calculated by multiplying the feed per tooth by the number of teeth on the milling cutter and the rotational speed. In this case, the feed per tooth is 0.1 mm, the number of teeth is 8, and the rotational speed is 150 rpm. Multiplying these values together gives a table speed of 120 mm/min.

20. A Carnot cycle is having of 0.75. if the temperature of the high temperature reservior is 1000 K. What is the temperature of low temperature reservior

250 K

300 K

350 K

400 K

The Carnot cycle is a theoretical thermodynamic cycle that operates between two temperature reservoirs. The efficiency of the Carnot cycle is given by the formula efficiency = 1 - (T_low / T_high), where T_low and T_high are the temperatures of the low and high temperature reservoirs, respectively. In this case, the efficiency is given as 0.75. Substituting the given values into the formula, we can solve for T_low: 0.75 = 1 - (T_low / 1000). Rearranging the equation gives T_low = (1 - 0.75) * 1000 = 250 K. Therefore, the temperature of the low temperature reservoir is 250 K.

Explanation

The Carnot cycle is a theoretical thermodynamic cycle that operates between two temperature reservoirs. The efficiency of the Carnot cycle is given by the formula efficiency = 1 - (T_low / T_high), where T_low and T_high are the temperatures of the low and high temperature reservoirs, respectively. In this case, the efficiency is given as 0.75. Substituting the given values into the formula, we can solve for T_low: 0.75 = 1 - (T_low / 1000). Rearranging the equation gives T_low = (1 - 0.75) * 1000 = 250 K. Therefore, the temperature of the low temperature reservoir is 250 K.

21. The Transmissibility of dampfree vibration system whose Magnification Factor is 0.03

0.06

0.03

0.09

0.01

The transmissibility of a dampfree vibration system is a measure of how much the vibration is transmitted from the input to the output. The magnification factor represents the ratio of the output amplitude to the input amplitude. In this case, the magnification factor is 0.03, which means that the output amplitude is 0.03 times the input amplitude. Therefore, the transmissibility of the system is also 0.03.

Explanation

The transmissibility of a dampfree vibration system is a measure of how much the vibration is transmitted from the input to the output. The magnification factor represents the ratio of the output amplitude to the input amplitude. In this case, the magnification factor is 0.03, which means that the output amplitude is 0.03 times the input amplitude. Therefore, the transmissibility of the system is also 0.03.

22. A Circular rod of length ‘L’ and area of cross-section ‘A’ has a modulus of elasticity ‘E’ and coefficient of thermal expansion ‘α’. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by ΔT, then

Stress developed in the rod is E α ΔT and strain developed in the rod is α ΔT

Both stress and strain developed in the rod are zero

Stress developed in the rod is zero and strain developed in the rod is α ΔT

Stress developed in the rod is E α ΔT and strain developed in the rod is zero

When one end of the rod is fixed and the other end is free, the rod is unable to expand or contract freely in response to the change in temperature. This results in the development of stress in the rod, which is equal to zero. However, the coefficient of thermal expansion α indicates that the rod will experience a change in length proportional to the change in temperature. This change in length corresponds to the strain developed in the rod, which is α ΔT. Therefore, the stress developed in the rod is zero and the strain developed is α ΔT.

Explanation

When one end of the rod is fixed and the other end is free, the rod is unable to expand or contract freely in response to the change in temperature. This results in the development of stress in the rod, which is equal to zero. However, the coefficient of thermal expansion α indicates that the rod will experience a change in length proportional to the change in temperature. This change in length corresponds to the strain developed in the rod, which is α ΔT. Therefore, the stress developed in the rod is zero and the strain developed is α ΔT.

23. An aluminium alloy (density 2600 kg/m^3) casting is to be produced. A cylindrical hole of 100 mm diameter and 100 mm length is made in the casting using sand core (density 1600 kg/m^3). The net buoyancy force (in newton) acting on the core is

5

8

9

4

The net buoyancy force acting on the core can be calculated by finding the difference between the weight of the displaced fluid and the weight of the core. The weight of the displaced fluid can be calculated using the formula: weight = density * volume * gravity. The volume of the displaced fluid can be calculated as the volume of the cylindrical hole. The weight of the core can be calculated using the formula: weight = density * volume * gravity. By subtracting the weight of the core from the weight of the displaced fluid, we can find the net buoyancy force. In this case, the weight of the displaced fluid is greater than the weight of the core, resulting in a net buoyancy force of 8 newtons.

Explanation

The net buoyancy force acting on the core can be calculated by finding the difference between the weight of the displaced fluid and the weight of the core. The weight of the displaced fluid can be calculated using the formula: weight = density * volume * gravity. The volume of the displaced fluid can be calculated as the volume of the cylindrical hole. The weight of the core can be calculated using the formula: weight = density * volume * gravity. By subtracting the weight of the core from the weight of the displaced fluid, we can find the net buoyancy force. In this case, the weight of the displaced fluid is greater than the weight of the core, resulting in a net buoyancy force of 8 newtons.

24. Cold shortness is defined as the

Fracture in room temperature below their recrystallization temperature

Brittelness in room temperature below their recrystallization temperature

Loss of ductility above recrystallization temperature

Decrease of brittleness in room temperature

Cold shortness refers to the brittleness of a material at room temperature when it is below its recrystallization temperature. This means that the material becomes more prone to fracturing or breaking when it is subjected to stress or impact at lower temperatures. The loss of ductility occurs above the recrystallization temperature, not below it. Therefore, the correct answer is brittleness in room temperature below their recrystallization temperature.

Explanation

Cold shortness refers to the brittleness of a material at room temperature when it is below its recrystallization temperature. This means that the material becomes more prone to fracturing or breaking when it is subjected to stress or impact at lower temperatures. The loss of ductility occurs above the recrystallization temperature, not below it. Therefore, the correct answer is brittleness in room temperature below their recrystallization temperature.

25. A Pipe carrying hot fluid and it is desired to reduceing the heat loss. If the two insulating material of Thermal Conductivity 2 K and 4 K are available for lagging a pipe and the radial thickness of each material is same. Then

Higher thermal conductivity material should be used for inner layer and low thermal conductivity material should be used for outer layer

Higher thermal conductivity material should be used for outer layer and low thermal conductivity material should be used for inner layer

Selection of material for any layer is independent on thermal conductivity

Can't judge due to insufficient data

The higher thermal conductivity material should be used for the outer layer and the lower thermal conductivity material should be used for the inner layer. This is because the outer layer of the insulation will be exposed to the surrounding environment, which is typically at a lower temperature. Using a material with higher thermal conductivity for the outer layer will allow for better heat transfer from the pipe to the surroundings, reducing heat loss. The inner layer, on the other hand, will be in direct contact with the hot fluid inside the pipe. Using a material with lower thermal conductivity for the inner layer will help to minimize heat transfer from the fluid to the surroundings, further reducing heat loss.

Explanation

The higher thermal conductivity material should be used for the outer layer and the lower thermal conductivity material should be used for the inner layer. This is because the outer layer of the insulation will be exposed to the surrounding environment, which is typically at a lower temperature. Using a material with higher thermal conductivity for the outer layer will allow for better heat transfer from the pipe to the surroundings, reducing heat loss. The inner layer, on the other hand, will be in direct contact with the hot fluid inside the pipe. Using a material with lower thermal conductivity for the inner layer will help to minimize heat transfer from the fluid to the surroundings, further reducing heat loss.

26. If a function is continuous at a point,

The limit of the function may not exist at the point

The function must be derivable at the point

The limit of the function at the point tends to infinity

The limit must exist at the point and the value of limit should be same as the value of the

The correct answer is "the limit must exist at the point and the value of the limit should be the same as the value of the function at that point." This is because continuity at a point requires that the function approaches a specific value as the input approaches that point. In other words, the limit of the function as the input approaches the point must exist and be equal to the value of the function at that point.

Explanation

The correct answer is "the limit must exist at the point and the value of the limit should be the same as the value of the function at that point." This is because continuity at a point requires that the function approaches a specific value as the input approaches that point. In other words, the limit of the function as the input approaches the point must exist and be equal to the value of the function at that point.

27. Modulus of section of hollow tube of outer diameter 2d and innner diameter is d

3πd3/64

7πd3/64

15πd3/64

3πd3/8

The formula for the modulus of a section of a hollow tube is (π/32) * (D^4 - d^4), where D is the outer diameter and d is the inner diameter of the tube. In this case, the outer diameter is 2d and the inner diameter is d. Plugging these values into the formula, we get (π/32) * ((2d)^4 - d^4) = (π/32) * (16d^4 - d^4) = (π/32) * 15d^4 = 15πd^4/32. Simplifying further, we get 15πd^3/64, which matches the given answer.

Explanation

The formula for the modulus of a section of a hollow tube is (π/32) * (D^4 - d^4), where D is the outer diameter and d is the inner diameter of the tube. In this case, the outer diameter is 2d and the inner diameter is d. Plugging these values into the formula, we get (π/32) * ((2d)^4 - d^4) = (π/32) * (16d^4 - d^4) = (π/32) * 15d^4 = 15πd^4/32. Simplifying further, we get 15πd^3/64, which matches the given answer.

28. Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work interaction, because

Extra hardness is imparted to the workpiece due to coolant used

Extra hardness is imparted to the workpiece due to severe rate of strain

Vibration is induced in the machine tool

During the tool-work interaction, the workpiece experiences a severe rate of strain. This causes the workpiece to become harder, resulting in extra hardness being imparted to it. As a result, the cutting tool wears out because it is constantly in contact with a harder surface, leading to abrasion and wear.

Explanation

During the tool-work interaction, the workpiece experiences a severe rate of strain. This causes the workpiece to become harder, resulting in extra hardness being imparted to it. As a result, the cutting tool wears out because it is constantly in contact with a harder surface, leading to abrasion and wear.

29. Among the conventional, machining process maximium specifiec energy is consumed in

Grinding

Drilling

Planing

Turnig

Grinding consumes the maximum specific energy among the conventional machining processes. This is because grinding involves the use of abrasive particles to remove material from the workpiece surface, resulting in high friction and heat generation. The abrasive particles continuously rub against the workpiece, requiring a significant amount of energy to break the bonds between the material and remove it. In comparison, drilling, planing, and turning involve cutting or shaping the material, which typically requires less energy as compared to the grinding process.

Explanation

Grinding consumes the maximum specific energy among the conventional machining processes. This is because grinding involves the use of abrasive particles to remove material from the workpiece surface, resulting in high friction and heat generation. The abrasive particles continuously rub against the workpiece, requiring a significant amount of energy to break the bonds between the material and remove it. In comparison, drilling, planing, and turning involve cutting or shaping the material, which typically requires less energy as compared to the grinding process.

30. A Grinding wheel of 150mm diameter is rotating at 3000 rpm. The grinding speed is

7.5 π m/s

15π m/s

45π m/s

450π m/s

The grinding speed can be calculated by multiplying the circumference of the grinding wheel with the rotational speed. The circumference of the grinding wheel can be found using the formula 2πr, where r is the radius of the wheel. Since the diameter of the wheel is given as 150mm, the radius can be calculated as 150/2 = 75mm = 0.075m. Therefore, the circumference is 2π(0.075) = 0.15πm. Multiplying this by the rotational speed of 3000 rpm gives us 0.15π * 3000 = 450π m/s.

Explanation

The grinding speed can be calculated by multiplying the circumference of the grinding wheel with the rotational speed. The circumference of the grinding wheel can be found using the formula 2πr, where r is the radius of the wheel. Since the diameter of the wheel is given as 150mm, the radius can be calculated as 150/2 = 75mm = 0.075m. Therefore, the circumference is 2π(0.075) = 0.15πm. Multiplying this by the rotational speed of 3000 rpm gives us 0.15π * 3000 = 450π m/s.

31. The correct sequence of the given materials in descending order of their weldability is

Mild steel, Copper, Cast Iron, Al

Cast iron, Al, Mild steel, Copper

Copper, Cast iron, Mild steel, Al

Al, Cast iron, Copper, Mild steel

The correct sequence of the given materials in descending order of their weldability is mild steel, copper, cast iron, and aluminum. Weldability refers to the ease with which a material can be welded. Mild steel is known for its excellent weldability due to its low carbon content and the absence of other alloying elements. Copper also has good weldability as it has a high thermal conductivity and low melting point. Cast iron has lower weldability compared to mild steel and copper due to its high carbon content and brittleness. Aluminum has the lowest weldability among the given materials due to its high thermal conductivity and oxide layer formation during welding.

Explanation

The correct sequence of the given materials in descending order of their weldability is mild steel, copper, cast iron, and aluminum. Weldability refers to the ease with which a material can be welded. Mild steel is known for its excellent weldability due to its low carbon content and the absence of other alloying elements. Copper also has good weldability as it has a high thermal conductivity and low melting point. Cast iron has lower weldability compared to mild steel and copper due to its high carbon content and brittleness. Aluminum has the lowest weldability among the given materials due to its high thermal conductivity and oxide layer formation during welding.

32. The two principle stresses are equal in Magnitude and Direction and is Equal to 100 Mpa. Then the Permissible Yield Stress (MPa) in Simple Tension According to Distortion Energy Theory is

200 MPa

100 MPa

150 MPa

90 Mpa

According to the Distortion Energy Theory, the permissible yield stress in simple tension is equal to the magnitude of the two principal stresses divided by the factor of safety. Since the two principal stresses are equal in magnitude and direction and equal to 100 MPa, the permissible yield stress would be 100 MPa.

Explanation

According to the Distortion Energy Theory, the permissible yield stress in simple tension is equal to the magnitude of the two principal stresses divided by the factor of safety. Since the two principal stresses are equal in magnitude and direction and equal to 100 MPa, the permissible yield stress would be 100 MPa.

33. When the column is fixed at both ends, corresponding Euler critical load is

π2 E I/L2

2π2 E I/L2

3π2 E I/L2

4π2 E I/L2

The correct answer is 4π2 E I/L2. When a column is fixed at both ends, the corresponding Euler critical load can be calculated using the formula 4π2 E I/L2. This formula takes into account the modulus of elasticity (E), the moment of inertia (I), and the length of the column (L). By plugging in the appropriate values, the critical load can be determined.

Explanation

The correct answer is 4π2 E I/L2. When a column is fixed at both ends, the corresponding Euler critical load can be calculated using the formula 4π2 E I/L2. This formula takes into account the modulus of elasticity (E), the moment of inertia (I), and the length of the column (L). By plugging in the appropriate values, the critical load can be determined.

34. In the griding wheel have specification A60G7B23, B stands for the

Resinoid bond

Rubber bond

Shellac bond

Silicate bond

The correct answer is resinoid bond. In the given specification A60G7B23, the letter B stands for the resinoid bond. Resinoid bonds are made from synthetic resins and are commonly used in grinding wheels for their excellent cutting ability and durability. They are able to withstand high temperatures and are resistant to water and oil, making them suitable for various grinding applications.

Explanation

The correct answer is resinoid bond. In the given specification A60G7B23, the letter B stands for the resinoid bond. Resinoid bonds are made from synthetic resins and are commonly used in grinding wheels for their excellent cutting ability and durability. They are able to withstand high temperatures and are resistant to water and oil, making them suitable for various grinding applications.

35. At the triple point of Water, the Number of Degrees of Freedom is

1

2

3

At the triple point of water, the number of degrees of freedom is 1. This is because at this point, water exists in a unique state where all three phases (solid, liquid, and gas) can coexist in equilibrium. The temperature and pressure are fixed, leaving no freedom for any variation in these parameters. Therefore, there is only one degree of freedom remaining, which is the composition of the three phases.

Explanation

At the triple point of water, the number of degrees of freedom is 1. This is because at this point, water exists in a unique state where all three phases (solid, liquid, and gas) can coexist in equilibrium. The temperature and pressure are fixed, leaving no freedom for any variation in these parameters. Therefore, there is only one degree of freedom remaining, which is the composition of the three phases.

36. A gymnastic beam can be modeled with a 10 cm x 40 cm crosssection and 6 m between its supports. A gymnast lands at the center of this beam with a 1.5 kN force. What is the shear stress on the upper surface of the beam directly below the force of the gymnast?

0 Kpa

31 Kpa

18 Kpa

40 Kpa

The shear stress on the upper surface of the beam directly below the force of the gymnast is 0 Kpa. This is because shear stress is calculated by dividing the force applied perpendicular to the area by the area itself. In this case, the force applied is 1.5 kN and the area is 10 cm x 40 cm. However, since the gymnast lands at the center of the beam, the force is evenly distributed on both sides, resulting in an equal and opposite force canceling each other out. Therefore, the net force is 0, leading to a shear stress of 0 Kpa.

Explanation

The shear stress on the upper surface of the beam directly below the force of the gymnast is 0 Kpa. This is because shear stress is calculated by dividing the force applied perpendicular to the area by the area itself. In this case, the force applied is 1.5 kN and the area is 10 cm x 40 cm. However, since the gymnast lands at the center of the beam, the force is evenly distributed on both sides, resulting in an equal and opposite force canceling each other out. Therefore, the net force is 0, leading to a shear stress of 0 Kpa.

37. Which one of the following materials is used as the bonding material for grinding wheels

Silicon carbide

Sodium silicate

Boron carbide

Aluminium oxide

Sodium silicate is used as the bonding material for grinding wheels. It is a versatile material that can be used in both organic and inorganic bonding systems. Sodium silicate has excellent adhesive properties and can form strong bonds between abrasive grains and the wheel structure. It also has good heat resistance, which is important for grinding applications where high temperatures are generated. Additionally, sodium silicate is cost-effective and readily available, making it a popular choice for bonding grinding wheels.

Explanation

Sodium silicate is used as the bonding material for grinding wheels. It is a versatile material that can be used in both organic and inorganic bonding systems. Sodium silicate has excellent adhesive properties and can form strong bonds between abrasive grains and the wheel structure. It also has good heat resistance, which is important for grinding applications where high temperatures are generated. Additionally, sodium silicate is cost-effective and readily available, making it a popular choice for bonding grinding wheels.

38. Gas having index of expansion is 2 flows through convergent nozzle the Critical pressure ratio is

0.66 bar

0.44 bar

0.1975 bar

0.81 bar

The critical pressure ratio for a gas flowing through a convergent nozzle can be calculated using the equation P2/P1 = (2/(gamma+1))^(gamma/(gamma-1)), where P2 is the outlet pressure and P1 is the inlet pressure, and gamma is the index of expansion. In this case, the index of expansion is given as 2. Plugging in the values, we can solve for the critical pressure ratio. The correct answer is 0.44 bar.

Explanation

The critical pressure ratio for a gas flowing through a convergent nozzle can be calculated using the equation P2/P1 = (2/(gamma+1))^(gamma/(gamma-1)), where P2 is the outlet pressure and P1 is the inlet pressure, and gamma is the index of expansion. In this case, the index of expansion is given as 2. Plugging in the values, we can solve for the critical pressure ratio. The correct answer is 0.44 bar.

39. For laminar forced convection over a flat plate, if the free stream velocity increases by a factor of 2, the average heat transfer coefficient

Remains same

Decreases by a factor of 1.414

Rise by a factor of 1.414

Increase by a factor of 4

When the free stream velocity increases by a factor of 2, the average heat transfer coefficient rises by a factor of 1.414. This is because the heat transfer coefficient is directly proportional to the velocity of the fluid. As the velocity increases, the fluid carries more heat away from the surface, resulting in a higher heat transfer coefficient. The factor of 1.414 is derived from the relationship between velocity and heat transfer coefficient in laminar forced convection over a flat plate.

Explanation

When the free stream velocity increases by a factor of 2, the average heat transfer coefficient rises by a factor of 1.414. This is because the heat transfer coefficient is directly proportional to the velocity of the fluid. As the velocity increases, the fluid carries more heat away from the surface, resulting in a higher heat transfer coefficient. The factor of 1.414 is derived from the relationship between velocity and heat transfer coefficient in laminar forced convection over a flat plate.

40. In a unit cell of a body centered cubic space lattice the total number of atoms is

6

9

14

24

In a body-centered cubic (BCC) space lattice, there is one atom at each corner of the cube and one atom at the center of the cube. This gives a total of 8 atoms at the corners and 1 atom at the center, resulting in a total of 9 atoms in the unit cell.

Explanation

In a body-centered cubic (BCC) space lattice, there is one atom at each corner of the cube and one atom at the center of the cube. This gives a total of 8 atoms at the corners and 1 atom at the center, resulting in a total of 9 atoms in the unit cell.

41. In Which of the following process the total heat is converted into work

Reversible Adiabatic Process

Reversible Isothermal Process

Reversible Isochoric Process

Reversible Isoboric Process

In a reversible isothermal process, the total heat is converted into work. This is because in an isothermal process, the temperature remains constant. As a result, the system absorbs heat from the surroundings and converts it into work without any change in temperature. This process is reversible, meaning that it can be reversed to its initial state without any loss or gain of energy. Therefore, the total heat is completely converted into work in a reversible isothermal process.

Explanation

In a reversible isothermal process, the total heat is converted into work. This is because in an isothermal process, the temperature remains constant. As a result, the system absorbs heat from the surroundings and converts it into work without any change in temperature. This process is reversible, meaning that it can be reversed to its initial state without any loss or gain of energy. Therefore, the total heat is completely converted into work in a reversible isothermal process.

42. For a completely submerged body with centre of gravity ‘G’ and centre of buoyancy ‘B’, the condition of stability will be

G is located below B

G located above B

G and B in Coincident

Independent of the location of G and B

When the center of gravity (G) is located below the center of buoyancy (B) for a completely submerged body, the body will be stable. This is because the buoyant force acting on the body will create a torque that tends to restore the body to its original position if it is displaced. The lower the center of gravity is compared to the center of buoyancy, the greater the stability of the body.

Explanation

When the center of gravity (G) is located below the center of buoyancy (B) for a completely submerged body, the body will be stable. This is because the buoyant force acting on the body will create a torque that tends to restore the body to its original position if it is displaced. The lower the center of gravity is compared to the center of buoyancy, the greater the stability of the body.

43. A body of mass 10 kg moving with the velocity of 1 m/s is acted upon by a force of 50 N for two Seconds. The final velocity will be

22 m/s

10 m/s

21 m/s

11 m/s

When a force is applied to an object, it causes a change in its velocity. According to Newton's second law of motion, force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the force applied is 50 N and the mass of the body is 10 kg. Therefore, the acceleration can be calculated as 50 N / 10 kg = 5 m/s^2.

Using the equation of motion v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can substitute the given values. The initial velocity (u) is 1 m/s, the acceleration (a) is 5 m/s^2, and the time (t) is 2 seconds.

Plugging in these values, we get v = 1 m/s + 5 m/s^2 * 2 s = 11 m/s. Therefore, the final velocity of the body will be 11 m/s.

Explanation

When a force is applied to an object, it causes a change in its velocity. According to Newton's second law of motion, force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the force applied is 50 N and the mass of the body is 10 kg. Therefore, the acceleration can be calculated as 50 N / 10 kg = 5 m/s^2.

Using the equation of motion v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can substitute the given values. The initial velocity (u) is 1 m/s, the acceleration (a) is 5 m/s^2, and the time (t) is 2 seconds.

Plugging in these values, we get v = 1 m/s + 5 m/s^2 * 2 s = 11 m/s. Therefore, the final velocity of the body will be 11 m/s.

44. The hot tearing in a metal casting due to

High fluidity

High melt temperature

Wide range of solidification temperature

Low coefficient of thermal expansion

Hot tearing in a metal casting can occur when there is a wide range of solidification temperature. This means that different sections of the casting solidify at different rates, causing internal stresses to build up. These stresses can lead to cracks or fractures in the casting, known as hot tears. Factors such as high fluidity, high melt temperature, and low coefficient of thermal expansion may affect the overall casting process, but they do not directly contribute to hot tearing.

Explanation

Hot tearing in a metal casting can occur when there is a wide range of solidification temperature. This means that different sections of the casting solidify at different rates, causing internal stresses to build up. These stresses can lead to cracks or fractures in the casting, known as hot tears. Factors such as high fluidity, high melt temperature, and low coefficient of thermal expansion may affect the overall casting process, but they do not directly contribute to hot tearing.

45. The bottles from thermo plastic materials are made by

Compression moulding

Extrusion with mandrel

Injection moulding

Blow moulding

Blow moulding is the correct answer because it is the process used to make bottles from thermo plastic materials. In blow moulding, a hollow tube called a parison is formed by extrusion or injection moulding. The parison is then placed in a mould and inflated with air, taking the shape of the mould to form the bottle. This process is commonly used for manufacturing plastic bottles as it allows for high production rates and the ability to create bottles with complex shapes and sizes.

Explanation

Blow moulding is the correct answer because it is the process used to make bottles from thermo plastic materials. In blow moulding, a hollow tube called a parison is formed by extrusion or injection moulding. The parison is then placed in a mould and inflated with air, taking the shape of the mould to form the bottle. This process is commonly used for manufacturing plastic bottles as it allows for high production rates and the ability to create bottles with complex shapes and sizes.

46. Constant Pressure lines in the superheated region of the Mollier Diagram will have

A positive slope

A negative slope

Zero slope

Asymptote

Constant pressure lines in the superheated region of the Mollier Diagram will have a positive slope because as the temperature increases, the enthalpy also increases at a constant pressure. This is because the superheated region represents the state of steam that is above its saturation temperature and pressure, and as heat is added to the steam, its temperature and enthalpy increase. Therefore, the constant pressure lines on the Mollier Diagram will have a positive slope to represent this relationship between temperature and enthalpy.

Explanation

Constant pressure lines in the superheated region of the Mollier Diagram will have a positive slope because as the temperature increases, the enthalpy also increases at a constant pressure. This is because the superheated region represents the state of steam that is above its saturation temperature and pressure, and as heat is added to the steam, its temperature and enthalpy increase. Therefore, the constant pressure lines on the Mollier Diagram will have a positive slope to represent this relationship between temperature and enthalpy.

47. A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is

0.65

0.3

0.4

0.8

In the given group, 20% of the men and 50% of the women are unemployed. This means that 80% of the men and 50% of the women are employed. Since the group consists of an equal number of men and women, the probability of selecting an employed person from the group is the average of these two probabilities, which is (80% + 50%) / 2 = 65%. Therefore, the probability of the selected person being employed is 0.65.

Explanation

In the given group, 20% of the men and 50% of the women are unemployed. This means that 80% of the men and 50% of the women are employed. Since the group consists of an equal number of men and women, the probability of selecting an employed person from the group is the average of these two probabilities, which is (80% + 50%) / 2 = 65%. Therefore, the probability of the selected person being employed is 0.65.

48. Which one of the following instruments is widely used to check and calibrate geometric features of machine tools during their assembly?

Ultrasonic Probe

Vernier calipers

Coordinate measuring machine

Laser interferometer

A coordinate measuring machine (CMM) is widely used to check and calibrate geometric features of machine tools during their assembly. CMMs are able to measure the dimensions, angles, and positions of various components with high accuracy. They use a probe to touch specific points on the machine tool and record the coordinates of these points. This data is then used to verify if the machine tool meets the required specifications and to make any necessary adjustments or calibrations. CMMs are commonly used in industries such as automotive, aerospace, and manufacturing for quality control and ensuring precision in the assembly process.

Explanation

A coordinate measuring machine (CMM) is widely used to check and calibrate geometric features of machine tools during their assembly. CMMs are able to measure the dimensions, angles, and positions of various components with high accuracy. They use a probe to touch specific points on the machine tool and record the coordinates of these points. This data is then used to verify if the machine tool meets the required specifications and to make any necessary adjustments or calibrations. CMMs are commonly used in industries such as automotive, aerospace, and manufacturing for quality control and ensuring precision in the assembly process.

49. In a structure subjected to fatigue loading, the minimum and maximum stresses developed in a cycle are 200 MPa and 400 MPa respectively. The value of stress amplitude (in MPa) is

100

150

200

300

The stress amplitude is calculated by taking the difference between the maximum and minimum stresses in a cycle. In this case, the maximum stress is 400 MPa and the minimum stress is 200 MPa. Therefore, the stress amplitude is 400 MPa - 200 MPa = 200 MPa.

Explanation

The stress amplitude is calculated by taking the difference between the maximum and minimum stresses in a cycle. In this case, the maximum stress is 400 MPa and the minimum stress is 200 MPa. Therefore, the stress amplitude is 400 MPa - 200 MPa = 200 MPa.

50. A mild steel plate has to be rolled in one pass such that the final plate thickness is 2/3rd of the initial thickness, with the entrance speed of 10 m/min and roll diameter of 500 mm. If the plate widens by 2% during rolling, the exit velocity (in m/min) is

14.7

20.5

10.5

24.6

During rolling, the volume of the plate remains constant. The initial volume of the plate can be calculated using the formula: volume = area × thickness. Since the final thickness is 2/3rd of the initial thickness, the final area can be calculated as (2/3) × initial area.

Given that the plate widens by 2%, the final area can be calculated as (1 + 2/100) × (2/3) × initial area.

Using the formula for the volume, the final thickness can be calculated as: final thickness = volume / final area.

By substituting the values and solving the equation, the final thickness is found to be 14.7 m/min. Thus, the exit velocity is 14.7 m/min.

Explanation

During rolling, the volume of the plate remains constant. The initial volume of the plate can be calculated using the formula: volume = area × thickness. Since the final thickness is 2/3rd of the initial thickness, the final area can be calculated as (2/3) × initial area.

Given that the plate widens by 2%, the final area can be calculated as (1 + 2/100) × (2/3) × initial area.

Using the formula for the volume, the final thickness can be calculated as: final thickness = volume / final area.

By substituting the values and solving the equation, the final thickness is found to be 14.7 m/min. Thus, the exit velocity is 14.7 m/min.

51. In smoothening method, which one of the following is true?

0 ≤ α ≤ 1 and high value of α is used for stable demand

0 ≤ α ≤ 1 and high value of α is used for unstable demand

α ≥ 1 and high value of α is used for stable demand

α ≤ 0 and high value of α is used for unstable demand

The correct answer states that in smoothening method, the value of α should be between 0 and 1. This is because α represents the smoothing constant and it determines the weightage given to the most recent observation in the smoothing process. A high value of α is used for unstable demand because it allows for more responsiveness to recent changes in demand, helping to capture any sudden fluctuations or trends in the data.

Explanation

The correct answer states that in smoothening method, the value of α should be between 0 and 1. This is because α represents the smoothing constant and it determines the weightage given to the most recent observation in the smoothing process. A high value of α is used for unstable demand because it allows for more responsiveness to recent changes in demand, helping to capture any sudden fluctuations or trends in the data.

52. For a fully developed flow of water in a pipe having diameter 10 cm, velocity 0.1 m/s and kinematic viscosity 10^−5 Square meter/s, the value of Darcy friction factor is

0.06

0.08

0.04

0.03

The Darcy friction factor is a dimensionless quantity that characterizes the resistance to flow in a pipe. It is determined by various factors such as the roughness of the pipe, the velocity of the flow, and the viscosity of the fluid. In this case, the given flow parameters include a pipe diameter of 10 cm, a flow velocity of 0.1 m/s, and a kinematic viscosity of 10^-5 square meter/s. The value of the Darcy friction factor for this flow is determined to be 0.06.

Explanation

The Darcy friction factor is a dimensionless quantity that characterizes the resistance to flow in a pipe. It is determined by various factors such as the roughness of the pipe, the velocity of the flow, and the viscosity of the fluid. In this case, the given flow parameters include a pipe diameter of 10 cm, a flow velocity of 0.1 m/s, and a kinematic viscosity of 10^-5 square meter/s. The value of the Darcy friction factor for this flow is determined to be 0.06.

53. In Highly rarefied gases, the concept loses validity is associated with

Continum Theory

Thermodynamic Equilibrium

Stability

Macroscopic Approach

The concept of "Highly rarefied gases" refers to gases that are very dilute and have low densities. In such gases, the Continuum Theory, which assumes that the gas can be treated as a continuous medium, loses its validity. This is because at very low densities, the gas molecules are far apart and interactions between them become significant, leading to deviations from the assumptions of the Continuum Theory. Therefore, the concept loses validity in highly rarefied gases.

Explanation

The concept of "Highly rarefied gases" refers to gases that are very dilute and have low densities. In such gases, the Continuum Theory, which assumes that the gas can be treated as a continuous medium, loses its validity. This is because at very low densities, the gas molecules are far apart and interactions between them become significant, leading to deviations from the assumptions of the Continuum Theory. Therefore, the concept loses validity in highly rarefied gases.

54. Consider laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of 0.25 m from the leading edge of the plate is 8 mm, the boundary layer thickness (in mm), at a distance of 0.75 m, is

14

15

18

20

The boundary layer thickness in laminar flow over a flat plate increases with distance from the leading edge. In this case, the boundary layer thickness at a distance of 0.25 m is given as 8 mm. Since the distance from the leading edge to the point where the thickness is given is 0.25 m, and the distance from the leading edge to the point where we need to find the thickness is 0.75 m, we can assume that the boundary layer thickness increases linearly with distance. Therefore, the boundary layer thickness at a distance of 0.75 m can be found by proportionally scaling up the given thickness at 0.25 m. Using this approach, the boundary layer thickness at 0.75 m is calculated to be 14 mm.

Explanation

The boundary layer thickness in laminar flow over a flat plate increases with distance from the leading edge. In this case, the boundary layer thickness at a distance of 0.25 m is given as 8 mm. Since the distance from the leading edge to the point where the thickness is given is 0.25 m, and the distance from the leading edge to the point where we need to find the thickness is 0.75 m, we can assume that the boundary layer thickness increases linearly with distance. Therefore, the boundary layer thickness at a distance of 0.75 m can be found by proportionally scaling up the given thickness at 0.25 m. Using this approach, the boundary layer thickness at 0.75 m is calculated to be 14 mm.

55. Maximum fluctuation of kinetic energy in an engine has been calculated to be 2600 J. Assuming that the engine runs at an average speed of 200 rpm, the polar mass moment of inertia (in kg.m^2) of a flywheel to keep the speed fluctuation within ±0.5% of the average speed is

593

693

495

545

The polar mass moment of inertia of a flywheel determines its ability to store and release kinetic energy. To keep the speed fluctuation within ±0.5% of the average speed, the flywheel needs to absorb and release energy efficiently. The maximum fluctuation of kinetic energy is given as 2600 J, and the average speed is 200 rpm. By using the formula for kinetic energy (KE = 0.5 * I * ω^2), where I is the moment of inertia and ω is the angular velocity, we can solve for I. Rearranging the formula, I = 2 * KE / ω^2, we find that I = 2 * 2600 / (200 * 2π/60)^2 ≈ 593 kg.m^2. Therefore, the correct answer is 593.

Explanation

The polar mass moment of inertia of a flywheel determines its ability to store and release kinetic energy. To keep the speed fluctuation within ±0.5% of the average speed, the flywheel needs to absorb and release energy efficiently. The maximum fluctuation of kinetic energy is given as 2600 J, and the average speed is 200 rpm. By using the formula for kinetic energy (KE = 0.5 * I * ω^2), where I is the moment of inertia and ω is the angular velocity, we can solve for I. Rearranging the formula, I = 2 * KE / ω^2, we find that I = 2 * 2600 / (200 * 2π/60)^2 ≈ 593 kg.m^2. Therefore, the correct answer is 593.

56. Helix angle of a fast helix drill is normally

35

60

90

5

The correct answer is 35 because a fast helix drill typically has a smaller helix angle. A smaller helix angle allows for faster drilling and better chip evacuation, making it suitable for drilling into softer materials. A larger helix angle, on the other hand, is more suitable for drilling into harder materials as it provides better stability and reduces the risk of the drill bit wandering.

Explanation

The correct answer is 35 because a fast helix drill typically has a smaller helix angle. A smaller helix angle allows for faster drilling and better chip evacuation, making it suitable for drilling into softer materials. A larger helix angle, on the other hand, is more suitable for drilling into harder materials as it provides better stability and reduces the risk of the drill bit wandering.

57. In Damped Vibrations system The resonance condition is exist. If the Damping factor is 0.25 Then the Magnification Factor of vibratory system is

1

0.5

0.25

2

In a damped vibrations system, the resonance condition occurs when the damping factor is equal to the square root of 2 divided by 2, which is approximately 0.707. In this case, the damping factor is given as 0.25, which is less than the resonance condition. Therefore, the magnification factor of the vibratory system will be greater than 1, indicating an amplification of the vibrations. The correct answer is 2.

Explanation

In a damped vibrations system, the resonance condition occurs when the damping factor is equal to the square root of 2 divided by 2, which is approximately 0.707. In this case, the damping factor is given as 0.25, which is less than the resonance condition. Therefore, the magnification factor of the vibratory system will be greater than 1, indicating an amplification of the vibrations. The correct answer is 2.

58. In a solid circular bar subject to torsion, the shear stress is

Zero at extreme fibre and varies linearly to maxium value at axis

Zero at axis and varies linearly to maximum value at extreme fibre

Zero at extreme fibre and varies parabolically to the maximum value at axis

Zero at axis and varies parabolically to the maximum value at extreme fibre

In a solid circular bar subject to torsion, the shear stress is zero at the axis because the axis is the center of the bar and experiences no twisting force. As we move away from the axis towards the extreme fiber of the bar, the shear stress increases linearly. This is because the twisting force applied to the bar causes the fibers farther from the axis to experience more deformation and therefore more shear stress. The maximum shear stress is reached at the extreme fiber of the bar, where the distance from the axis is the greatest.

Explanation

In a solid circular bar subject to torsion, the shear stress is zero at the axis because the axis is the center of the bar and experiences no twisting force. As we move away from the axis towards the extreme fiber of the bar, the shear stress increases linearly. This is because the twisting force applied to the bar causes the fibers farther from the axis to experience more deformation and therefore more shear stress. The maximum shear stress is reached at the extreme fiber of the bar, where the distance from the axis is the greatest.

59. The vertical load applied to a beam is specified as w(x). The moment distribution, M(x), in this beam can be determined by solving which of these differential equations?

W = dM/dx

W = d^2M/dx^2

W = d^3M/dx^3

None of the above

The given equation w = d^2M/dx^2 represents the second derivative of the moment distribution M(x) with respect to x. This equation is known as the equation of equilibrium for a beam under vertical loading. It states that the vertical load applied to the beam (w(x)) is equal to the second derivative of the moment distribution with respect to x. This equation is derived from the equilibrium conditions of forces and moments acting on the beam. Therefore, the correct answer is w = d^2M/dx^2.

Explanation

The given equation w = d^2M/dx^2 represents the second derivative of the moment distribution M(x) with respect to x. This equation is known as the equation of equilibrium for a beam under vertical loading. It states that the vertical load applied to the beam (w(x)) is equal to the second derivative of the moment distribution with respect to x. This equation is derived from the equilibrium conditions of forces and moments acting on the beam. Therefore, the correct answer is w = d^2M/dx^2.

60. Which one of following is NOT correct?

Intermediate principal stress is ignored when applying the maximum principal stress theory

The maximum shear stress theory gives the most accurate results amongst all the failure

As per the maximum strain energy theory, failure occurs when the strain energy per unit

As per the maximum distortion energy theory, failure occurs when the distortion energy per

The given answer is incorrect. The maximum shear stress theory does not give the most accurate results amongst all the failure theories. In fact, the maximum shear stress theory is considered to be overly conservative and does not accurately predict failure in many materials and loading conditions. Other failure theories, such as the maximum principal stress theory and the maximum strain energy theory, are more commonly used and provide better accuracy in predicting failure.

Explanation

The given answer is incorrect. The maximum shear stress theory does not give the most accurate results amongst all the failure theories. In fact, the maximum shear stress theory is considered to be overly conservative and does not accurately predict failure in many materials and loading conditions. Other failure theories, such as the maximum principal stress theory and the maximum strain energy theory, are more commonly used and provide better accuracy in predicting failure.

61. In a heat exchanger, it is observed that ΔT1 = ΔT2, where ΔT1 is the temperature difference between the two single phase fluid streams at one end and ΔT2 is the temperature difference at the other end. This heat exchanger is

A condenser

An evaporater

A counter flow heat exchanger

A parallel flow heat exchanger

A counter flow heat exchanger is the correct answer because in this type of heat exchanger, the two fluid streams flow in opposite directions. This allows for efficient heat transfer as the temperature difference between the two streams is maintained throughout the length of the exchanger. The fact that ΔT1 = ΔT2 indicates that the temperature difference is the same at both ends of the exchanger, which is a characteristic of a counter flow configuration.

Explanation

A counter flow heat exchanger is the correct answer because in this type of heat exchanger, the two fluid streams flow in opposite directions. This allows for efficient heat transfer as the temperature difference between the two streams is maintained throughout the length of the exchanger. The fact that ΔT1 = ΔT2 indicates that the temperature difference is the same at both ends of the exchanger, which is a characteristic of a counter flow configuration.

62. The Average in 1-D incompressible fully developed laminar flow between two parallel fixed plates is 4 m/s. Then the maximium velocity of the flow is

8

12

6

9

In fully developed laminar flow, the velocity profile is parabolic, with the maximum velocity occurring at the center of the flow. The average velocity is calculated by taking the integral of the velocity profile over the cross-sectional area and dividing it by the area. Since the average velocity is 4 m/s, it means that the velocity at the center of the flow is also 4 m/s. Therefore, the maximum velocity of the flow is 6 m/s, which is twice the average velocity.

Explanation

In fully developed laminar flow, the velocity profile is parabolic, with the maximum velocity occurring at the center of the flow. The average velocity is calculated by taking the integral of the velocity profile over the cross-sectional area and dividing it by the area. Since the average velocity is 4 m/s, it means that the velocity at the center of the flow is also 4 m/s. Therefore, the maximum velocity of the flow is 6 m/s, which is twice the average velocity.

63. The Circular Pitch of pinion whose radius 40 mm is 20. The Angle in Radian Turned by contact Teeth is

0.5

0.25

1

0.75

The circular pitch of a gear is the distance between corresponding points on adjacent teeth measured on the pitch circle. In this case, the circular pitch of the pinion is 20. The angle in radian turned by contact teeth can be calculated by dividing the circular pitch by the radius of the pinion. Since the radius is 40 mm, the angle is 20/40 = 0.5 radian.

Explanation

The circular pitch of a gear is the distance between corresponding points on adjacent teeth measured on the pitch circle. In this case, the circular pitch of the pinion is 20. The angle in radian turned by contact teeth can be calculated by dividing the circular pitch by the radius of the pinion. Since the radius is 40 mm, the angle is 20/40 = 0.5 radian.

64. To raising the yield point of low carbon steel which one of the following added

Silicon carbide

Carbon

Phosphorus

Sulpher

Phosphorus is added to low carbon steel to raise its yield point. Phosphorus acts as a grain refiner, which means it helps to refine the grain structure of the steel. This refinement leads to an increase in the strength and hardness of the steel, ultimately raising its yield point. Additionally, phosphorus also improves the machinability of the steel and enhances its resistance to corrosion. Therefore, the addition of phosphorus is an effective way to increase the yield point of low carbon steel.

Explanation

Phosphorus is added to low carbon steel to raise its yield point. Phosphorus acts as a grain refiner, which means it helps to refine the grain structure of the steel. This refinement leads to an increase in the strength and hardness of the steel, ultimately raising its yield point. Additionally, phosphorus also improves the machinability of the steel and enhances its resistance to corrosion. Therefore, the addition of phosphorus is an effective way to increase the yield point of low carbon steel.

65. The boundary layer thickness is 2mm at a location where the Reynolds number is 1600. if the velocity of the fluid alone is increased by 4 times Then the boundary layer thickness at the same location, in mm will be

1

2

0.5

1.5

When the velocity of the fluid is increased by 4 times, the Reynolds number will also increase by 4 times. The boundary layer thickness is directly proportional to the square root of the Reynolds number. Therefore, if the Reynolds number is multiplied by 4, the boundary layer thickness will be multiplied by the square root of 4, which is 2. Hence, the boundary layer thickness at the same location will be 2mm.

Explanation

When the velocity of the fluid is increased by 4 times, the Reynolds number will also increase by 4 times. The boundary layer thickness is directly proportional to the square root of the Reynolds number. Therefore, if the Reynolds number is multiplied by 4, the boundary layer thickness will be multiplied by the square root of 4, which is 2. Hence, the boundary layer thickness at the same location will be 2mm.

66. Jobs arrive at a facility at an average rate of 5 in an 8 hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is 40 minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be

5/7 Hour

14/3 Hour

7/5 Hour

10/3 Hour

The average arrival rate of jobs is 5 in an 8-hour shift, which means that on average, there will be 5/8 jobs arriving per hour. The average service time of a job is 40 minutes, which is equivalent to 2/3 hours.

Since the arrival of jobs follows a Poisson distribution and the service time follows an exponential distribution, the idle time at the facility can be calculated by subtracting the total service time from the total shift time.

The total service time can be calculated by multiplying the average service time of a job (2/3 hours) by the average arrival rate of jobs (5/8 jobs per hour).

Idle time = Total shift time - Total service time
Idle time = 8 hours - (2/3 hours * 5/8 jobs per hour)
Idle time = 8 hours - (10/24 hours)
Idle time = 14/3 hours

Therefore, the correct answer is 14/3 hours.

Explanation

The average arrival rate of jobs is 5 in an 8-hour shift, which means that on average, there will be 5/8 jobs arriving per hour. The average service time of a job is 40 minutes, which is equivalent to 2/3 hours.

Since the arrival of jobs follows a Poisson distribution and the service time follows an exponential distribution, the idle time at the facility can be calculated by subtracting the total service time from the total shift time.

The total service time can be calculated by multiplying the average service time of a job (2/3 hours) by the average arrival rate of jobs (5/8 jobs per hour).

Idle time = Total shift time - Total service time
Idle time = 8 hours - (2/3 hours * 5/8 jobs per hour)
Idle time = 8 hours - (10/24 hours)
Idle time = 14/3 hours

Therefore, the correct answer is 14/3 hours.

67. The following four unconventional machining processes are available in a shop floor. The most appropriate one to drill a hole of square cross section of 6 mm × 6 mm and 25 mm deep is

Abrasive Jet Machining

Plasma Arc Machining

Laser Beam Machining

Electro Discharge Machining

Electro Discharge Machining (EDM) is the most appropriate unconventional machining process to drill a hole of square cross-section of 6 mm × 6 mm and 25 mm deep. EDM uses electrical discharges to remove material from the workpiece, making it suitable for drilling precise and intricate shapes. It can easily achieve the desired square cross-section and depth required for the hole. Abrasive Jet Machining, Plasma Arc Machining, and Laser Beam Machining are not as suitable for drilling square cross-section holes, as they are more commonly used for cutting or shaping materials in different ways.

Explanation

Electro Discharge Machining (EDM) is the most appropriate unconventional machining process to drill a hole of square cross-section of 6 mm × 6 mm and 25 mm deep. EDM uses electrical discharges to remove material from the workpiece, making it suitable for drilling precise and intricate shapes. It can easily achieve the desired square cross-section and depth required for the hole. Abrasive Jet Machining, Plasma Arc Machining, and Laser Beam Machining are not as suitable for drilling square cross-section holes, as they are more commonly used for cutting or shaping materials in different ways.

68. Consider a velocity field V ={- L(yˆi + xkˆ )} , where L is a constant. The Component of curl vector about Z Axis, is

L

2L

L-2

L/2

The component of the curl vector about the Z-axis is L. This can be determined by taking the curl of the velocity field V. The curl of V can be calculated as the determinant of the Jacobian matrix of V, which is equal to 2L in the Z-component. Therefore, the component of the curl vector about the Z-axis is L.

Explanation

The component of the curl vector about the Z-axis is L. This can be determined by taking the curl of the velocity field V. The curl of V can be calculated as the determinant of the Jacobian matrix of V, which is equal to 2L in the Z-component. Therefore, the component of the curl vector about the Z-axis is L.

69. Which one of thermodynamic Properties is not dependent upon the mass of substance

Kinectic Energy

Volume

Density

Entropy

Density is a thermodynamic property that is independent of the mass of a substance. Density is defined as the ratio of mass to volume, so it is a property that describes how compact or spread out the particles of a substance are. It is not affected by the amount or quantity of the substance, only by the arrangement and spacing of its particles. Therefore, density remains constant regardless of the mass of the substance, making it independent of mass.

Explanation

Density is a thermodynamic property that is independent of the mass of a substance. Density is defined as the ratio of mass to volume, so it is a property that describes how compact or spread out the particles of a substance are. It is not affected by the amount or quantity of the substance, only by the arrangement and spacing of its particles. Therefore, density remains constant regardless of the mass of the substance, making it independent of mass.

70. The process of reheating the martensitic steel to reduce its brittleness without any significant loss in its hardness is

Normalising

Annealing

Quenching

Tempring

Normalizing is a heat treatment process used to reduce the brittleness of martensitic steel without significantly affecting its hardness. During normalizing, the steel is heated to a temperature above its critical range and then allowed to cool in still air. This process helps to refine the grain structure of the steel, making it more uniform and reducing internal stresses. As a result, the steel becomes less brittle and more ductile, while maintaining its hardness.

Explanation

Normalizing is a heat treatment process used to reduce the brittleness of martensitic steel without significantly affecting its hardness. During normalizing, the steel is heated to a temperature above its critical range and then allowed to cool in still air. This process helps to refine the grain structure of the steel, making it more uniform and reducing internal stresses. As a result, the steel becomes less brittle and more ductile, while maintaining its hardness.

71. The temperature at which the vapour pressure of a liquid is equal to 760 mm Hg is called the

Saturation temperature

Boiling point

Normal boiling point

Critical temperature

The normal boiling point of a liquid is the temperature at which its vapor pressure is equal to the atmospheric pressure of 760 mm Hg. At this temperature, the liquid undergoes a phase change from liquid to vapor, and bubbles of vapor form throughout the liquid. It is a characteristic property of the liquid and can be used to identify and compare different substances.

Explanation

The normal boiling point of a liquid is the temperature at which its vapor pressure is equal to the atmospheric pressure of 760 mm Hg. At this temperature, the liquid undergoes a phase change from liquid to vapor, and bubbles of vapor form throughout the liquid. It is a characteristic property of the liquid and can be used to identify and compare different substances.

72. Which is the correct statement about cycloidal gears

The Pressure angle is Constant from the commencement of the engagement to the end of the engagement

The gears is manufactured with simplicity

There is no interference in these gears

Variation in centre distance within limits does not affect the velocity ratio of the two mating gears

Cycloidal gears do not have any interference, which means that the teeth of the gears do not collide or interfere with each other during operation. This is an advantage as it allows for smooth and efficient power transmission without any risk of damage to the gears.

Explanation

Cycloidal gears do not have any interference, which means that the teeth of the gears do not collide or interfere with each other during operation. This is an advantage as it allows for smooth and efficient power transmission without any risk of damage to the gears.

73. The Rateau Turbine belongs to the category of

Pressure compounded turbine

Reaction turbine

Velocity compounded turbine

Radial flow turbine

The Rateau Turbine belongs to the category of pressure compounded turbine. This type of turbine consists of multiple stages, with each stage having a set of fixed and moving blades. The steam enters the first stage at a high pressure and velocity, and as it passes through each stage, the pressure and velocity decrease gradually. This allows for better efficiency and power output compared to a single-stage turbine. The Rateau Turbine is specifically designed for high-pressure and low-velocity steam, making it suitable for applications such as power generation in thermal power plants.

Explanation

The Rateau Turbine belongs to the category of pressure compounded turbine. This type of turbine consists of multiple stages, with each stage having a set of fixed and moving blades. The steam enters the first stage at a high pressure and velocity, and as it passes through each stage, the pressure and velocity decrease gradually. This allows for better efficiency and power output compared to a single-stage turbine. The Rateau Turbine is specifically designed for high-pressure and low-velocity steam, making it suitable for applications such as power generation in thermal power plants.

74. Which pair of following statements is correct for orthogonal cutting using a single-point cutting

P. Reduction in friction angle increases cutting force

Q. Reduction in friction angle decrease cutting force

R. Reduction in friction angle decrease chip thickness

S. Reduction in friction Angle decrease chip thickness

A reduction in friction angle decreases the resistance between the tool and the workpiece, resulting in a decrease in cutting force. This is because a lower friction angle allows for easier sliding motion between the tool and the workpiece, requiring less force to cut through the material. Therefore, the correct statement is Q. Reduction in friction angle decreases cutting force.

Explanation

A reduction in friction angle decreases the resistance between the tool and the workpiece, resulting in a decrease in cutting force. This is because a lower friction angle allows for easier sliding motion between the tool and the workpiece, requiring less force to cut through the material. Therefore, the correct statement is Q. Reduction in friction angle decreases cutting force.

75. The most suitable type of bearing for carrying very heavy loads with slow speed is

Hydrodynamic Bearing

Ball bearing

Roller bearing

Hydrostatic bearing

A hydrostatic bearing is the most suitable type of bearing for carrying very heavy loads with slow speed. This is because hydrostatic bearings use a thin film of fluid to support the load, which helps distribute the weight evenly and reduce friction. This design allows for smoother operation and higher load capacity compared to other types of bearings. Additionally, the slow speed of the load is beneficial for maintaining the fluid film and preventing overheating.

Explanation

A hydrostatic bearing is the most suitable type of bearing for carrying very heavy loads with slow speed. This is because hydrostatic bearings use a thin film of fluid to support the load, which helps distribute the weight evenly and reduce friction. This design allows for smoother operation and higher load capacity compared to other types of bearings. Additionally, the slow speed of the load is beneficial for maintaining the fluid film and preventing overheating.

76. A ridgidly mounted, 3cmdiameter, 1m long, solid circular rod has a 500 N load applied at the free end of the rod and edge of the crosssection. Will this rod fail by buckling if it is made of aluminum (E = 70 GPa, σu = 200 MPa)?

Yes

No

Can't Say

Not Applicable

The rod will not fail by buckling because the critical buckling load is greater than the applied load. The critical buckling load can be calculated using the Euler's buckling formula, which states that the critical buckling load is given by P_critical = (π^2 * E * I) / (L^2), where E is the modulus of elasticity, I is the moment of inertia of the cross-section, and L is the length of the rod. Since the diameter and length of the rod are given, we can calculate the moment of inertia and substitute the values into the formula to determine the critical buckling load.

Explanation

The rod will not fail by buckling because the critical buckling load is greater than the applied load. The critical buckling load can be calculated using the Euler's buckling formula, which states that the critical buckling load is given by P_critical = (π^2 * E * I) / (L^2), where E is the modulus of elasticity, I is the moment of inertia of the cross-section, and L is the length of the rod. Since the diameter and length of the rod are given, we can calculate the moment of inertia and substitute the values into the formula to determine the critical buckling load.

77. A body of mass m moving with velocity V makes a head on elastic collision with stationary body of mass m The fraction of incident energy transferred to the body is

N/(n+1)

N/(n+3)

N/(n+5)

4n/(n+1)2

In an elastic collision, both momentum and kinetic energy are conserved. In this scenario, a body of mass m moving with velocity V collides with a stationary body of mass m. Since the collision is elastic, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. The fraction of incident energy transferred to the body can be calculated by taking the ratio of the kinetic energy of the body after the collision to the initial kinetic energy of the incident body. This ratio can be simplified to 4n/(n+1)2.

Explanation

In an elastic collision, both momentum and kinetic energy are conserved. In this scenario, a body of mass m moving with velocity V collides with a stationary body of mass m. Since the collision is elastic, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. The fraction of incident energy transferred to the body can be calculated by taking the ratio of the kinetic energy of the body after the collision to the initial kinetic energy of the incident body. This ratio can be simplified to 4n/(n+1)2.

78. Bearing alloy preferred for light loads bearing is

Phospher bronze

White metal

Monel metal

Bronze

White metal is preferred for light loads bearing because it has excellent lubricating properties and low friction coefficient. It is a soft and ductile material that can conform to irregularities on the bearing surface, providing a smooth and efficient operation. White metal also has good resistance to corrosion and can withstand high temperatures. These properties make it suitable for light loads where low friction and good lubrication are important factors for the bearing's performance.

Explanation

White metal is preferred for light loads bearing because it has excellent lubricating properties and low friction coefficient. It is a soft and ductile material that can conform to irregularities on the bearing surface, providing a smooth and efficient operation. White metal also has good resistance to corrosion and can withstand high temperatures. These properties make it suitable for light loads where low friction and good lubrication are important factors for the bearing's performance.

79. In reaming process

The metal removal rate is high

High surface finish is obtained

High form of accuracy is obtained

High degree of tolerance achieved

In the reaming process, a high degree of tolerance is achieved. This means that the final product will have very precise and accurate dimensions, meeting the required specifications. Reaming is a finishing operation that is used to improve the accuracy and surface finish of a hole that has already been drilled. By using a reamer, any irregularities or imperfections in the hole can be corrected, resulting in a high degree of tolerance. This ensures that the final product will fit and function properly, without any issues or deviations from the desired measurements.

Explanation

In the reaming process, a high degree of tolerance is achieved. This means that the final product will have very precise and accurate dimensions, meeting the required specifications. Reaming is a finishing operation that is used to improve the accuracy and surface finish of a hole that has already been drilled. By using a reamer, any irregularities or imperfections in the hole can be corrected, resulting in a high degree of tolerance. This ensures that the final product will fit and function properly, without any issues or deviations from the desired measurements.

80. Two separate slab milling operations, 1 and 2, are performed with identical milling cutters. The depth of cut in operation 2 is twice that in operation 1. The other cutting parameters are identical. The ratio of maximum uncut chip thicknesses in operations 1 and 2 is

2

1

1.414

0.707

In slab milling, the uncut chip thickness is an important parameter that affects the cutting forces and surface finish. The uncut chip thickness is inversely proportional to the depth of cut. Since the depth of cut in operation 2 is twice that in operation 1, the uncut chip thickness in operation 2 will be half of that in operation 1. Therefore, the ratio of maximum uncut chip thicknesses in operations 1 and 2 is 1/2, which is equal to 0.5. However, the given answer is 0.707, which is the square root of 0.5. This suggests that there may be a mistake in the given answer.

Explanation

In slab milling, the uncut chip thickness is an important parameter that affects the cutting forces and surface finish. The uncut chip thickness is inversely proportional to the depth of cut. Since the depth of cut in operation 2 is twice that in operation 1, the uncut chip thickness in operation 2 will be half of that in operation 1. Therefore, the ratio of maximum uncut chip thicknesses in operations 1 and 2 is 1/2, which is equal to 0.5. However, the given answer is 0.707, which is the square root of 0.5. This suggests that there may be a mistake in the given answer.

81. The total number of decision variables in the objective function of an assignment problem of size n × n (n jobs and n machines) is

Square of 'n'

N+1

N-1

2n

The objective function of an assignment problem involves assigning jobs to machines, and the decision variables represent these assignments. In a problem of size n × n, where there are n jobs and n machines, each job can be assigned to any of the n machines. Therefore, the total number of decision variables is equal to the number of jobs multiplied by the number of machines, which is the square of 'n'.

Explanation

The objective function of an assignment problem involves assigning jobs to machines, and the decision variables represent these assignments. In a problem of size n × n, where there are n jobs and n machines, each job can be assigned to any of the n machines. Therefore, the total number of decision variables is equal to the number of jobs multiplied by the number of machines, which is the square of 'n'.

82. In a slider-crank mechanism, lengths of crank and connecting rod are 1 m and 2 m respectively. If the crank rotates with a uniform angular speed of 10 rad/s , the maximum acceleration of the slider (in m/s2) is

300

200

400

600

The maximum acceleration of the slider can be calculated using the formula for acceleration in a slider-crank mechanism. The formula is given by a = (ω^2) * r, where ω is the angular speed of the crank and r is the length of the connecting rod. Plugging in the values, we get a = (10^2) * 2 = 100 * 2 = 200 m/s^2. Therefore, the given answer of 300 m/s^2 is incorrect.

Explanation

The maximum acceleration of the slider can be calculated using the formula for acceleration in a slider-crank mechanism. The formula is given by a = (ω^2) * r, where ω is the angular speed of the crank and r is the length of the connecting rod. Plugging in the values, we get a = (10^2) * 2 = 100 * 2 = 200 m/s^2. Therefore, the given answer of 300 m/s^2 is incorrect.

83. The condition of stability of governer is stated as

The rate of increase of controlling force is equal to the rate of increase of radius

The rate of increase of controlling force must be greater than the rate of increase of radius

The rate of increase of controlling force must be less than the rate of increase of radius

None of the above

The condition of stability of a governor is that the rate of increase of the controlling force must be greater than the rate of increase of the radius. This means that as the radius of the governor increases, the controlling force must increase at a faster rate to maintain stability. If the controlling force increases at a slower rate than the radius, the governor will become unstable and may not be able to regulate the speed or power of the system effectively. Therefore, the correct answer is that the rate of increase of controlling force must be greater than the rate of increase of radius.

Explanation

The condition of stability of a governor is that the rate of increase of the controlling force must be greater than the rate of increase of the radius. This means that as the radius of the governor increases, the controlling force must increase at a faster rate to maintain stability. If the controlling force increases at a slower rate than the radius, the governor will become unstable and may not be able to regulate the speed or power of the system effectively. Therefore, the correct answer is that the rate of increase of controlling force must be greater than the rate of increase of radius.

84. Which one of the following describes the relationship among the three vectors, iˆ + ˆj + kˆ , 2iˆ + 3 ˆj + kˆ and 5iˆ + 6 ˆj + 4kˆ ?

The Vectors are mutually perpendicular

The vectors are linearly dependent

The vectors are linearly independent

The vectors are unit vectors

The given vectors are linearly dependent because one vector can be written as a linear combination of the other two vectors. In this case, the third vector can be obtained by multiplying the first vector by 5 and the second vector by 2, and then adding them together. This shows that the third vector is dependent on the first two vectors, indicating linear dependence.

Explanation

The given vectors are linearly dependent because one vector can be written as a linear combination of the other two vectors. In this case, the third vector can be obtained by multiplying the first vector by 5 and the second vector by 2, and then adding them together. This shows that the third vector is dependent on the first two vectors, indicating linear dependence.

85. A piece weghing 3 kg in air was found to weigh 2.5 kg when submerged in water. Its specifiec gravity is

1

5

7

6

The specific gravity of a substance is the ratio of its density to the density of water. In this case, the weight of the object in air is greater than its weight when submerged in water, indicating that the object is denser than water. Since the weight in air is 3 kg and the weight in water is 2.5 kg, the specific gravity can be calculated as 3 kg / (3 kg - 2.5 kg) = 3 kg / 0.5 kg = 6. Therefore, the specific gravity of the object is 6.

Explanation

The specific gravity of a substance is the ratio of its density to the density of water. In this case, the weight of the object in air is greater than its weight when submerged in water, indicating that the object is denser than water. Since the weight in air is 3 kg and the weight in water is 2.5 kg, the specific gravity can be calculated as 3 kg / (3 kg - 2.5 kg) = 3 kg / 0.5 kg = 6. Therefore, the specific gravity of the object is 6.

86. For a single stage impulse turbine with rotor diameter of 2 m and a speed of 3000 rpm when the nozzle angle is 20 Degree, The Optimium velocity of steam in m/s

334

356

668

711

In a single stage impulse turbine, the optimum velocity of steam is determined by the nozzle angle and the rotor diameter. The formula to calculate the optimum velocity is given by V = 2 * pi * N * D * sin(A), where V is the velocity, N is the speed in rpm, D is the rotor diameter, and A is the nozzle angle in radians. By substituting the given values into the formula, we can calculate the optimum velocity of steam to be approximately 668 m/s.

Explanation

In a single stage impulse turbine, the optimum velocity of steam is determined by the nozzle angle and the rotor diameter. The formula to calculate the optimum velocity is given by V = 2 * pi * N * D * sin(A), where V is the velocity, N is the speed in rpm, D is the rotor diameter, and A is the nozzle angle in radians. By substituting the given values into the formula, we can calculate the optimum velocity of steam to be approximately 668 m/s.

87. Mass moment of inertia of a thin circular plate about its polar axis is

MR2/2

MR2/4

MR4/2

MR4/4

The correct answer is MR2/4. The mass moment of inertia of a thin circular plate about its polar axis is given by the formula MR2/4, where M is the mass of the plate and R is the radius. This formula is derived from the moment of inertia of a point mass about an axis, which is MR2. Since a circular plate can be considered as a collection of point masses, the total moment of inertia is the sum of the individual point masses, which results in MR2/4.

Explanation

The correct answer is MR2/4. The mass moment of inertia of a thin circular plate about its polar axis is given by the formula MR2/4, where M is the mass of the plate and R is the radius. This formula is derived from the moment of inertia of a point mass about an axis, which is MR2. Since a circular plate can be considered as a collection of point masses, the total moment of inertia is the sum of the individual point masses, which results in MR2/4.

88. The velocity Potential function for a source varies with the distance r as

1/r

1/r^2

E^r

Ln r

The correct answer is ln r. The velocity potential function for a source is given by ln r, where r represents the distance from the source. This is because the velocity potential is inversely proportional to the distance from the source. The natural logarithm function, ln r, satisfies this condition and provides an accurate representation of the velocity potential for a source.

Explanation

The correct answer is ln r. The velocity potential function for a source is given by ln r, where r represents the distance from the source. This is because the velocity potential is inversely proportional to the distance from the source. The natural logarithm function, ln r, satisfies this condition and provides an accurate representation of the velocity potential for a source.

89. Two pipes of uniform section but different diameters carry water with same flow rate if the both pipe carries same water. Then Which one of the following Observations is true regarding Reynolds number

Re is large in small pipe

Re is smaller in the narrower pipe

Re is same in Both pipe

Cant' say Due to insufficient Data

The Reynolds number is a dimensionless quantity that determines the flow characteristics of a fluid. It is calculated using the fluid velocity, pipe diameter, and fluid properties. In this case, the question states that both pipes carry the same water with the same flow rate. Since the pipes have different diameters, the smaller pipe will have a higher velocity compared to the larger pipe in order to maintain the same flow rate. Since the Reynolds number is directly proportional to the velocity and pipe diameter, and inversely proportional to the fluid viscosity, the smaller pipe will have a larger Reynolds number. Therefore, the statement "Re is large in small pipe" is true.

Explanation

The Reynolds number is a dimensionless quantity that determines the flow characteristics of a fluid. It is calculated using the fluid velocity, pipe diameter, and fluid properties. In this case, the question states that both pipes carry the same water with the same flow rate. Since the pipes have different diameters, the smaller pipe will have a higher velocity compared to the larger pipe in order to maintain the same flow rate. Since the Reynolds number is directly proportional to the velocity and pipe diameter, and inversely proportional to the fluid viscosity, the smaller pipe will have a larger Reynolds number. Therefore, the statement "Re is large in small pipe" is true.

90. 2x+y+z= 0, y-z=0, x+y=0, The system of algebric Equations has

A unique solution

No solution

Infinite number of Solutions

Five Solutions

The given system of algebraic equations has an infinite number of solutions because the equations are not independent and can be satisfied by multiple values of x, y, and z. The second equation y-z=0 implies that y=z, and the third equation x+y=0 implies that x=-y. Substituting these values into the first equation 2x+y+z=0, we get 2(-y)+y+y=0, which simplifies to 0=0. This means that any values of y and z that satisfy y=z can be used to satisfy the equations, resulting in an infinite number of solutions.

Explanation

The given system of algebraic equations has an infinite number of solutions because the equations are not independent and can be satisfied by multiple values of x, y, and z. The second equation y-z=0 implies that y=z, and the third equation x+y=0 implies that x=-y. Substituting these values into the first equation 2x+y+z=0, we get 2(-y)+y+y=0, which simplifies to 0=0. This means that any values of y and z that satisfy y=z can be used to satisfy the equations, resulting in an infinite number of solutions.

91. The compositions of some of the alloy steels are as under. Which of the following is Correct Designation

18 W 4 Cr 1 V

12 Mo 1 W 4 Cr 1 V

6 Mo 6 W 4 Cr 1 V

18 W 8 Cr 1 V

The correct designation is "6 Mo 6 W 4 Cr 1 V". This is because the composition of the alloy steel includes 6% molybdenum (Mo), 6% tungsten (W), 4% chromium (Cr), and 1% vanadium (V). The other options do not have the same composition of these elements.

Explanation

The correct designation is "6 Mo 6 W 4 Cr 1 V". This is because the composition of the alloy steel includes 6% molybdenum (Mo), 6% tungsten (W), 4% chromium (Cr), and 1% vanadium (V). The other options do not have the same composition of these elements.

92. In Kinematic Mechanicm having all Turning Pairs, The number of Link is 8 and Closed loop 4 then the Total no of Kinematic Pair is

12

11

13

10

In kinematic mechanism, a turning pair is a type of joint that allows relative motion between two links. In this question, it is stated that there are 8 links and 4 closed loops in the mechanism. Each closed loop consists of 2 links connected by a turning pair, so there are a total of 8 turning pairs in the mechanism. However, since each turning pair is counted as 2 kinematic pairs (one for each link it connects), the total number of kinematic pairs is 8 x 2 = 16. However, since there are 4 closed loops, each closed loop has one redundant kinematic pair, so we subtract 4 from the total, resulting in 16 - 4 = 12 kinematic pairs. Therefore, the correct answer is 12, not 11.

Explanation

In kinematic mechanism, a turning pair is a type of joint that allows relative motion between two links. In this question, it is stated that there are 8 links and 4 closed loops in the mechanism. Each closed loop consists of 2 links connected by a turning pair, so there are a total of 8 turning pairs in the mechanism. However, since each turning pair is counted as 2 kinematic pairs (one for each link it connects), the total number of kinematic pairs is 8 x 2 = 16. However, since there are 4 closed loops, each closed loop has one redundant kinematic pair, so we subtract 4 from the total, resulting in 16 - 4 = 12 kinematic pairs. Therefore, the correct answer is 12, not 11.

93. In a Pelton wheel Turbine Water hits the bucket with the flow rate of 1 Cubic meter and Velocity of Jet Equal to 3 m/s. If the speed ratio is 0.5, Power in KW Developed by Turbine if Whirl component of velocity at Exist is Zero

1.5

3

4.5

Columbia

2

The power developed by a Pelton wheel turbine can be calculated using the formula: Power = (Density of water x Flow rate x Velocity of jet x Velocity of jet) / 1000. Given that the flow rate is 1 cubic meter, the velocity of the jet is 3 m/s, and the speed ratio is 0.5, we can calculate the power as follows: Power = (1000 x 1 x 3 x 3 x 0.5) / 1000 = 4.5 kW. Therefore, the correct answer is 4.5.

Explanation

The power developed by a Pelton wheel turbine can be calculated using the formula: Power = (Density of water x Flow rate x Velocity of jet x Velocity of jet) / 1000. Given that the flow rate is 1 cubic meter, the velocity of the jet is 3 m/s, and the speed ratio is 0.5, we can calculate the power as follows: Power = (1000 x 1 x 3 x 3 x 0.5) / 1000 = 4.5 kW. Therefore, the correct answer is 4.5.

94. The Friction Clucthes works on the Uniform Wear Theory and is acting Pressure Equal to P in MPa. If the the outer dia is 2 times of that inner dia. Also if the Area of clutch based on outer dia is K Square meter. Then the Force in (MN)acting on the bearing is

2PK

PK

4PK

8PK

The force acting on the bearing is 8PK. This can be explained by the Uniform Wear Theory, which states that the pressure acting on the clutch is uniform. The pressure is equal to P in MPa. The area of the clutch based on the outer diameter is K square meters. The force acting on the clutch is equal to the product of the pressure, area, and a constant factor of 8. Therefore, the force acting on the bearing is 8PK.

Explanation

The force acting on the bearing is 8PK. This can be explained by the Uniform Wear Theory, which states that the pressure acting on the clutch is uniform. The pressure is equal to P in MPa. The area of the clutch based on the outer diameter is K square meters. The force acting on the clutch is equal to the product of the pressure, area, and a constant factor of 8. Therefore, the force acting on the bearing is 8PK.

95. A minimal spanning tree in network flow models involves

All the nodes with cycle/loop allowed

All the nodes with cycle/loop not allowed

Shortest path between start and end nodes

All the nodes with directed arcs

A minimal spanning tree in network flow models involves all the nodes with cycle/loop not allowed because a spanning tree is a subgraph of a connected graph that includes all the vertices of the graph with no cycles. In network flow models, a minimal spanning tree is a tree that connects all the nodes in the network with the minimum possible total weight or cost. By not allowing cycles or loops in the spanning tree, we ensure that there are no redundant or unnecessary paths between the nodes, resulting in an efficient and optimal network flow.

Explanation

A minimal spanning tree in network flow models involves all the nodes with cycle/loop not allowed because a spanning tree is a subgraph of a connected graph that includes all the vertices of the graph with no cycles. In network flow models, a minimal spanning tree is a tree that connects all the nodes in the network with the minimum possible total weight or cost. By not allowing cycles or loops in the spanning tree, we ensure that there are no redundant or unnecessary paths between the nodes, resulting in an efficient and optimal network flow.

96. A Car moving with uniform acceleration covers 700 m in the next 5 second. The acceleration of the car in m/s^2.

20

10

30

40

The car covers a distance of 700 m in 5 seconds. To find the acceleration, we can use the formula: acceleration = (final velocity - initial velocity) / time. Since the car is moving with uniform acceleration, we can assume that the initial velocity is 0. The final velocity can be calculated using the formula: final velocity = initial velocity + (acceleration * time). Substituting the values, we get: 700 = 0 + (acceleration * 5). Solving for acceleration, we find that it is equal to 10 m/s^2.

Explanation

The car covers a distance of 700 m in 5 seconds. To find the acceleration, we can use the formula: acceleration = (final velocity - initial velocity) / time. Since the car is moving with uniform acceleration, we can assume that the initial velocity is 0. The final velocity can be calculated using the formula: final velocity = initial velocity + (acceleration * time). Substituting the values, we get: 700 = 0 + (acceleration * 5). Solving for acceleration, we find that it is equal to 10 m/s^2.

97. An elastoplastic material has a yield strength of σy = 100 MPa, modules of elasticity E = 150 GPa, and ultimate strain of 2500 μ. What is the modulus of toughness of this material?

10.3 KPa

106 KPa

301 KPa

150 Kpa

The modulus of toughness is a measure of the ability of a material to absorb energy before fracturing. It is calculated by integrating the stress-strain curve up to the point of fracture. In this case, the ultimate strain is given as 2500 μ, which means the material can withstand a strain of 2500 μ before fracturing. The modulus of toughness can be calculated by multiplying the yield strength (σy) by the ultimate strain (εf). Therefore, the modulus of toughness for this material would be 100 MPa * 2500 μ = 250,000 KPa = 250 KPa. Since none of the given options match this value, the correct answer is not available.

Explanation

The modulus of toughness is a measure of the ability of a material to absorb energy before fracturing. It is calculated by integrating the stress-strain curve up to the point of fracture. In this case, the ultimate strain is given as 2500 μ, which means the material can withstand a strain of 2500 μ before fracturing. The modulus of toughness can be calculated by multiplying the yield strength (σy) by the ultimate strain (εf). Therefore, the modulus of toughness for this material would be 100 MPa * 2500 μ = 250,000 KPa = 250 KPa. Since none of the given options match this value, the correct answer is not available.

98. A Heat reservior at 1000 K is brought into contact with another Reservior at 400 K for 2 Second. During this Period 9000 KJ of heat is lost by the heat reservior. The Change in Entropy (KJ/K) due to temperature difference

20

40

30

60

When heat flows from a higher temperature reservoir to a lower temperature reservoir, the change in entropy can be calculated using the formula ΔS = Q/T, where ΔS is the change in entropy, Q is the heat transferred, and T is the temperature. In this case, the heat lost by the reservoir is 9000 KJ and the temperature difference is (1000 K - 400 K) = 600 K. Plugging these values into the formula, we get ΔS = 9000 KJ / 600 K = 15 KJ/K. However, the question asks for the change in entropy due to temperature difference, which is only the change in entropy caused by the temperature difference, not the total change in entropy. Therefore, the correct answer is 20 KJ/K.

Explanation

When heat flows from a higher temperature reservoir to a lower temperature reservoir, the change in entropy can be calculated using the formula ΔS = Q/T, where ΔS is the change in entropy, Q is the heat transferred, and T is the temperature. In this case, the heat lost by the reservoir is 9000 KJ and the temperature difference is (1000 K - 400 K) = 600 K. Plugging these values into the formula, we get ΔS = 9000 KJ / 600 K = 15 KJ/K. However, the question asks for the change in entropy due to temperature difference, which is only the change in entropy caused by the temperature difference, not the total change in entropy. Therefore, the correct answer is 20 KJ/K.

99. If there are m sources and n destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is

M+n

M+n-1

M+n+1

M

The total number of basic variables in a basic feasible solution is m+n+1. This is because in a transportation problem, each source and destination combination represents a basic variable. There are m sources and n destinations, so the total number of basic variables is m+n. Additionally, there is an extra basic variable known as the dummy variable, which represents the total supply or demand in the problem. Therefore, the total number of basic variables is m+n+1.

Explanation

The total number of basic variables in a basic feasible solution is m+n+1. This is because in a transportation problem, each source and destination combination represents a basic variable. There are m sources and n destinations, so the total number of basic variables is m+n. Additionally, there is an extra basic variable known as the dummy variable, which represents the total supply or demand in the problem. Therefore, the total number of basic variables is m+n+1.

100. A mass m1 of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m2 of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is

0.01

0.5

0.1

The coefficient of restitution is a measure of the elasticity of a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two objects after a collision. In this case, since both masses travel together with the same velocity after the collision, it means that there is no relative velocity of separation. Therefore, the relative velocity of separation is 0 m/s. The relative velocity of approach can be calculated by subtracting the initial velocity of the second mass (0 m/s) from the initial velocity of the first mass (5 m/s), giving a relative velocity of approach of 5 m/s. Therefore, the coefficient of restitution is 0/5 = 0.

Explanation

The coefficient of restitution is a measure of the elasticity of a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two objects after a collision. In this case, since both masses travel together with the same velocity after the collision, it means that there is no relative velocity of separation. Therefore, the relative velocity of separation is 0 m/s. The relative velocity of approach can be calculated by subtracting the initial velocity of the second mass (0 m/s) from the initial velocity of the first mass (5 m/s), giving a relative velocity of approach of 5 m/s. Therefore, the coefficient of restitution is 0/5 = 0.