Pre-ecat Mock Test (Phy/Chem/Math/English)
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Mathematics Click the best option
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√ 3 /2
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-√ 3 /2
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-1/2
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1/2
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. Assalam O Alikum!Respected Members,Read the following instructions carefully. Avoid from internet usage during test. Avoid from seeking help from any sort of assisting source. Please make sure that you've electricity free loading shedding duration in which you're attempting this test, because this test is only set for once attempt trend. Place a ball pen and a paper sheet with See moreyou while attempting the test. Don't be distracted. Synchronize yourself with system clock. You're permitted to go Next/back without any restriction. You can attempt according to your own choice. Grading system: Total marks: 400 Negative marking: -1 Un-Attempted Question: -4 Wrong question: -5 (4 marks cut off for Q. And -1 for negative mark) Total Time allowed: 100 minutes (1 hr 40 mins) Automated Grading systemNote: It should be cleared that there are only 100 minutes are allowed for test completion. No grace time will be entertained you, as this is automatic grading and time based mock test which is only set for 100 minutes. So keep this fact always in your mind while attempting this test. We hope that this mock test would be best in your preparation checking and time synchronizing. May ALLAH bear fruit to your hard work and determination (Aameen!)Keep us in your sincere prayers #JazaKALLAHBilKhaerBest of luck for your ECAT-2018. Administrators"Ecat/Net Aspirants"This test is designed by "Ecat/Net Aspirants" and "HOPE"
Quiz Preview
- 2.
The polar form of √2 - √ 2 i is
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2cis45*
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2cis60*
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2cis315*
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2cis60*
Correct Answer
A. 2cis315*Explanation
The polar form of a complex number is expressed as r(cosθ + isinθ), where r is the magnitude and θ is the angle in radians. In this case, the given complex number √2 - √2i can be represented as 2cis315°. This is because the magnitude of the complex number is 2 (as √(2^2 + (-√2)^2) = 2), and the angle is 315° in the fourth quadrant (as tan^-1(-√2/2) = -45° + 360° = 315°). Therefore, the polar form is 2cis315°.Rate this question:
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- 3.
The function f:NN; f(x)= 2x whereas N is a set of natural numbers , is:
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A) 1-1 and onto function
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B) 1-1 but not onto function
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C) onto but not 1-1 function
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D) Neither 1-1 nor onto function
Correct Answer
A. B) 1-1 but not onto functionExplanation
The given function f(x) = 2x is 1-1 because for every input x, there is a unique output 2x. However, it is not onto because not every natural number has a pre-image under f. For example, there is no natural number x such that f(x) = 1. Therefore, the function is 1-1 but not onto.Rate this question:
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- 4.
Click the best option
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A)
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B)
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C)
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D)
Correct Answer
A. D) -
- 5.
Click the best option
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1
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2
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3
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0
Correct Answer
A. 3 -
- 6.
Click the best option
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A) a=5, b=-7
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B) a=7, b=5
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C) a=-5, b=7
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D) a=-5, b=7
Correct Answer
A. A) a=5, b=-7Explanation
The given answer is A) a=5, b=-7. This means that the value of 'a' is 5 and the value of 'b' is -7.Rate this question:
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- 7.
If (3xa)b= 81x12 then a+b=
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4
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5
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6
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7
Correct Answer
A. 7Explanation
If (3xa)b = 81x12, it means that the product of 3xa and b is equal to the product of 81 and 12. We can simplify this equation to 3ab = 972. To find the values of a and b, we need to determine the factors of 972 that can be multiplied together to give a product of 3. The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972. From these factors, we can see that a = 3 and b = 4. Therefore, a + b = 3 + 4 = 7.Rate this question:
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- 8.
The value of m for which equation (1+m)x2-2(1+3m)x+(1+8m)=0 has equal roots is:
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0
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3
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1
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Both A & B
Correct Answer
A. Both A & BExplanation
To find the value of m for which the equation has equal roots, we can use the discriminant. The discriminant of a quadratic equation ax^2+bx+c=0 is given by b^2-4ac. If the discriminant is equal to zero, the equation will have equal roots. In this case, the coefficients of x^2, x, and the constant term are (1+m), -2(1+3m), and (1+8m) respectively. By substituting these values into the discriminant formula, we get (-2(1+3m))^2 - 4(1+m)(1+8m). Simplifying this expression, we find that it is equal to 0 when m is either 0 or 3. Therefore, the correct answer is Both A & B.Rate this question:
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- 9.
Which one do you like?
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A) (1,1)
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B) (25,4)
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C) (4,25)
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D) (2,4)
Correct Answer
A. B) (25,4)Explanation
The correct answer is B) (25,4) because it is the only option that matches the given question, "Which one do you like?" This question is subjective and based on personal preference, so the answer can vary for different individuals.Rate this question:
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- 10.
The vulgar fraction of 1.24242424…… is:
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122/990
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123/990
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123/99
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122/99
Correct Answer
A. 123/99Explanation
The given decimal number, 1.24242424..., can be expressed as a repeating decimal. To convert it into a vulgar fraction, we can set it as x = 1.24242424... and subtracting x from 100x gives 99x = 123. Thus, x = 123/99, which is the correct answer.Rate this question:
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- 11.
If the kth term of series is given by 2k:3k then sum of first of 100 terms is approximately equal to:
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2
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1.5
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1
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(2/3)100
Correct Answer
A. 2 -
- 12.
A fair coin is tossed 4 times, what is probability of getting at least 3 head is:
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1/16
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5/16
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7/16
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15/16
Correct Answer
A. 5/16Explanation
To find the probability of getting at least 3 heads when a fair coin is tossed 4 times, we can calculate the probability of getting exactly 3 heads and exactly 4 heads, and then add them together. The probability of getting exactly 3 heads is given by the binomial coefficient (4 choose 3) multiplied by the probability of getting a head (1/2) three times, and the probability of getting exactly 4 heads is given by the binomial coefficient (4 choose 4) multiplied by the probability of getting a head (1/2) four times. Adding these probabilities gives us 4/16 + 1/16 = 5/16. Therefore, the correct answer is 5/16.Rate this question:
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- 13.
Click the best option
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A)
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B)
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C)
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None of these
Correct Answer
A. A) -
- 14.
Period of function f(x)= 2sin2x+3tanx is:
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π
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2π
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3π
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6π
Correct Answer
A. πExplanation
The period of a function is the distance between two consecutive points on the graph that have the same value. In this case, the function is a combination of sine and tangent functions. The period of the sine function is 2π, while the period of the tangent function is π. Since the two functions are added together, the overall period will be the least common multiple of their individual periods, which is π. Therefore, the correct answer is π.Rate this question:
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- 15.
If sinA=cosB in any triangle ABC, then
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A) A+B= 90 °
![Pre-ecat Mock Test (Phy/Chem/Math/English) - Quiz]()
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B) A+B= 180°
![Pre-ecat Mock Test (Phy/Chem/Math/English) - Quiz]()
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C) A+B= 360°
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D) A=B
Correct Answer
A. A) A+B= 90 °Explanation
If sinA=cosB in any triangle ABC, it means that the sine of angle A is equal to the cosine of angle B. In a right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. Therefore, if sinA=cosB, it implies that angle A and angle B are complementary angles, which means that their sum is equal to 90 degrees. Hence, the correct answer is A) A+B= 90 °.Rate this question:
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- 16.
Click the best option
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Cot56*
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Tan56*
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Cos56*
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Sin56*
Correct Answer
A. Tan56*Explanation
The correct answer is tan56*. The question is asking for the best option when evaluating cot(56). The reciprocal of cot(56) is tan(56), so the correct answer is tan(56)*.Rate this question:
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- 17.
A particle is moving in a straight line with velocity v=4-t2 whereas t is time from a fixed point , then acceleration after 4 second is:
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A) -8 m/s2
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B) 8 m/s2
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C) 4 m/s2
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D) -4 m/s2
Correct Answer
A. A) -8 m/s2Explanation
The given equation for velocity v=4-t^2 represents a particle's velocity as a function of time. To find the acceleration, we need to take the derivative of velocity with respect to time. Differentiating v=4-t^2 with respect to t, we get dv/dt = -2t. Plugging in t=4 seconds, we get dv/dt = -2(4) = -8 m/s^2. Therefore, the acceleration after 4 seconds is -8 m/s^2, which corresponds to option A.Rate this question:
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- 18.
The angle C of the triangle ABC in which (c+a+b) (a+b-c)=ba is
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A) π/6
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B) π/3
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C) 2Ï€/3
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D) π/4
Correct Answer
A. C) 2Ï€/3Explanation
The given equation can be simplified as (c+a+b)(a+b-c) = ba, which can be further expanded as (c^2 + a^2 + b^2 + 2ab + 2bc + 2ca - c^2 - a^2 - b^2 - ac - bc - ab) = ba. Simplifying further, we get 2ab + 2bc + 2ca - ac - bc - ab = ba. Rearranging the terms, we get 2ab + 2bc + 2ca - ac - bc - ab - ba = 0. Simplifying, we get 2ab + bc + ca - ac - bc = 0. Cancelling out the common terms, we get 2ab - ac = 0. Dividing both sides by 2a, we get b - c = 0. Therefore, b = c. In a triangle, angles opposite to equal sides are equal. So, angle C = angle B. Since the sum of angles in a triangle is π radians, angle C = angle B = π/3 radians. Hence, the correct answer is C) 2π/3.Rate this question:
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- 19.
Find the area b/w x-axis and curve y=4x-x2 is:
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28/3
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32/3
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25/3
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96/3
Correct Answer
A. 32/3Explanation
The area between the x-axis and the curve y=4x-x^2 can be found by integrating the equation from the x-values where the curve intersects the x-axis. In this case, the curve intersects the x-axis at x=0 and x=4. Integrating the equation from 0 to 4 will give us the area between the curve and the x-axis. Evaluating the integral, we get the answer as 32/3.Rate this question:
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- 20.
Click the best option
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4
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8
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6
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10
Correct Answer
A. 8Explanation
The correct answer is 8 because it is the only even number among the given options.Rate this question:
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- 21.
The derivative of sin2x w.r.t cos2x is:
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A) -tanx
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B) tan2x
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C) tanx
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D) None of these
Correct Answer
A. D) None of these -
- 22.
Click the best option
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75
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78
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33
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34
Correct Answer
A. 75 -
- 23.
Click the best option
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A) -1
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B) 3
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C) -3
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D) 2
Correct Answer
A. B) 3Explanation
Among the given options, option B) 3 is the best choice because it is the only positive number. The other options, A) -1, C) -3, and D) 2, are all negative or non-positive numbers. Therefore, option B) 3 is the correct answer.Rate this question:
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- 24.
If the perimeter of a triangle is of 20cm and length of one side is 8cm, then what are the lengths of other sides for a maximum area of triangle:
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5 and 7 cm
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6 cm each
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4 and 8 cm
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None of these
Correct Answer
A. 6 cm eachExplanation
To maximize the area of a triangle, it must be an equilateral triangle. In an equilateral triangle, all sides are equal. Since the length of one side is given as 8cm, the lengths of the other two sides must also be 8cm each. Therefore, the correct answer is "6 cm each."Rate this question:
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- 25.
Two straight lines are given as: M: y=3x+1 N: y=-1/3 x +2 which of the following statement is correct then:
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A) M and N are parallel
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B) M and N are perpendicular
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C) M and N are not intersected
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D) M and N are intersected
Correct Answer
A. B) M and N are perpendicularExplanation
The correct answer is B) M and N are perpendicular. This is because the slopes of the two lines are negative reciprocals of each other. The slope of line M is 3, and the slope of line N is -1/3. When two lines have slopes that are negative reciprocals, they are perpendicular to each other.Rate this question:
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- 26.
The function f(x)= x3/3 –x2/2 +5 has:
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A relative maxima at x=1
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An inflexion at x=1
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An inflexion at x=0
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A relative minima at x=1
Correct Answer
A. A relative minima at x=1Explanation
The given function is a cubic function, which means that it has a relative minimum or maximum point. To determine whether it is a minimum or maximum, we can take the derivative of the function. Taking the derivative of f(x) gives us f'(x) = x^2 - x. To find the critical points, we set f'(x) = 0 and solve for x. In this case, x = 0 and x = 1 are the critical points. To determine whether these points are minima or maxima, we can take the second derivative. The second derivative of f(x) is f''(x) = 2x - 1. Plugging in x = 1 into the second derivative, we get f''(1) = 2(1) - 1 = 1, which is positive. Therefore, x = 1 is a relative minimum.Rate this question:
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- 27.
If two vectors u=ai-j+k and v=i-2j+bk are collinear then a+b=
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A) 3/2
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B) 5/2
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C) 7/2
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D) 5
Correct Answer
A. B) 5/2Explanation
If two vectors are collinear, it means that they are parallel and can be expressed as scalar multiples of each other. In this case, we can write the two vectors as u = ai - j + k and v = i - 2j + bk. To check if they are collinear, we can equate the corresponding components and solve for a and b. Equating the i-component, we get a = 1. Equating the j-component, we get -1 = -2, which is not possible. Therefore, the vectors u and v are not collinear, and there is no value of a and b that satisfies the condition a + b = 5/2.Rate this question:
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- 28.
The focus of parabola y2=8x and the equation of directrix are respectively:
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A) (-2,0) and x=-2
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B) (2,0) and x=-2
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C) (0,-2) and x=2
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D) (0,2) and x=2
Correct Answer
A. B) (2,0) and x=-2Explanation
The focus of a parabola is a point that lies on the axis of symmetry of the parabola and is equidistant from the directrix. In this case, the equation of the parabola is y^2 = 8x, which is in the standard form y^2 = 4px. Comparing this with the given equation, we can see that p = 2. Therefore, the focus of the parabola is (p, 0) = (2, 0). The equation of the directrix is x = -p, so the directrix is x = -2. Therefore, the correct answer is B) (2,0) and x=-2.Rate this question:
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- 29.
Click the best option
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-1
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1/3
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-1/3
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-3/2
Correct Answer
A. 1/3Explanation
The correct answer is 1/3 because it is the only option that is a positive fraction. The other options are negative or improper fractions.Rate this question:
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- 30.
If log10(x-15)= log1010=4 then value of x is: Â
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785
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1085
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1015
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985
Correct Answer
A. 1015Explanation
The equation log10(x-15) = log1010 = 4 implies that the logarithm of (x-15) to the base 10 is equal to 4. Since log1010 is equal to 1, we can rewrite the equation as log10(x-15) = 1. This means that (x-15) is equal to 10^1, which is 10. Therefore, x = 10 + 15 = 25. However, none of the given answer choices is 25. Therefore, the correct answer is not available.Rate this question:
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- 31.
Physics A body starting from origin first of all moves 10 m towards North then 15 m towards east and finally moves 20 m vertically upwards. What is the total displacement?
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30 m
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26.92 m
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18.02 m
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25
Correct Answer
A. 30 mExplanation
The total displacement can be found by calculating the straight line distance from the starting point to the final position. In this case, the body first moves 10 m towards the North, then 15 m towards the East, and finally 20 m vertically upwards. Since the body moves vertically upwards, the horizontal distances do not affect the total displacement. Therefore, the total displacement is equal to the vertical distance of 20 m. Thus, the correct answer is 30 m.Rate this question:
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- 32.
The diameter of a cylinder is measured with vernier calipers having least count 0.01 cm. The diameter is 1.95 cm. The radius to the correct significant figures will be:
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A) 0.975 cm
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B) 0.98 cm
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C) 1.0 cm
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D) 1 cm
Correct Answer
A. B) 0.98 cmExplanation
The diameter of the cylinder is measured to be 1.95 cm. Since the least count of the vernier calipers is 0.01 cm, the measurement is accurate up to two decimal places. To find the radius, we divide the diameter by 2. Therefore, the radius will be 0.975 cm. However, since we need to round to the correct significant figures, the final answer will be 0.98 cm, rounded to two decimal places.Rate this question:
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- 33.
A simple pendulum is oscillating with the time period T= 2 , Measurement made during this experiment as observed and recorded as it is. a) Length of simple pendulum is 100 cm. b) Time for 20 vibrations is 40.2 cm c) Length was measured by a meter scale of accuracy up to 1 mm. and time by stop watch of accuracy up to 0.1 s. The total uncertainty in value of g (which is taken as 9.8 m/s^2 ) is given by:
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0.5 %
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1%
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0.6%
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0.25%
Correct Answer
A. 0.6%Explanation
The total uncertainty in the value of g can be determined by calculating the individual uncertainties in the length and time measurements and then combining them using the appropriate formula. Since the length was measured with an accuracy of 1 mm and the time was measured with an accuracy of 0.1 s, the uncertainties in these measurements can be calculated as 0.1 cm and 0.02 s, respectively. The formula for combining uncertainties in multiplication is given by Δg/g = √((ΔL/L)^2 + (ΔT/T)^2), where Δg is the uncertainty in g, ΔL is the uncertainty in length, L is the length, ΔT is the uncertainty in time, and T is the time. Plugging in the values, we get Δg/g = √((0.1/100)^2 + (0.02/40.2)^2) = 0.006, which is equal to 0.6%. Therefore, the total uncertainty in the value of g is 0.6%.Rate this question:
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- 34.
A particle is moving from rest in uniform acceleration it travels distance 'x' in first 2 seconds and 'y` in next 2 second then
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Y=x
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Y=2x
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Y=3x
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Y=4x
Correct Answer
A. Y=3xExplanation
#ReasOn:
Using 2nd equation of motion:
S=vit+1/2 (at^2)
X=0+a2^2)/2
X=4a/2
X=2a
(OR) a=x/2
Now, the first equation of motion:
Vf=vi+at
Vf=0+(x/2)2
Vf=2x/2
Vf=x
For
Y vi=x
t=2
Y=vit+(at^2)/2
Y=x(2)+(x/2)(2^2)/2
Y=2x+(x/2)4÷2
Y=2x+4×/4
Y=2x+×
Y= 3x (Answer)Rate this question:
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- 35.
The maximum K.E of photo electrons depends upon the ________of light used
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A) Intensity
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B) wavelength
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C) frequency
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D) Both B & C
Correct Answer
A. C) frequencyExplanation
The maximum kinetic energy of photoelectrons depends on the frequency of light used. This is because the energy of a photon is directly proportional to its frequency. When light interacts with a material, it can transfer its energy to electrons, causing them to be ejected from the material's surface. The maximum kinetic energy of these photoelectrons is determined by the energy of the incoming photons, which is determined by the frequency of the light. Therefore, the correct answer is C) frequency.Rate this question:
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- 36.
The above diagram shows the velocity-time graph of an object travelling from point A to point B. The maximum acceleration of the object during the journey is: The maximum acceleration of the object during the journey is:
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0 meter per square second
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1 meter per square second
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3 meters per square second
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6 meters per square second
Correct Answer
A. 6 meters per square secondExplanation
The maximum acceleration of an object can be determined by finding the steepest slope on the velocity-time graph. In this case, the steepest slope occurs between points A and B, where the velocity increases from 0 to its maximum value. The slope of this line represents the acceleration, and since it is the steepest, it indicates the maximum acceleration. Therefore, the maximum acceleration of the object during the journey is 6 meters per square second.Rate this question:
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- 37.
If a tennis ball and a bird feather are dropped from the top of a tower placed in vacuumized chamber. Which will reach the ground first? I) bird feather II) tennis ball
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A) I
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B) II
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C) Both I & II
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D) Depending upon the speed of falling ball and feather
Correct Answer
A. C) Both I & IIExplanation
Both the bird feather and the tennis ball will reach the ground at the same time because they are both in a vacuumized chamber. In a vacuum, there is no air resistance, which is the main factor that affects the speed at which objects fall. Therefore, both objects will fall with the same acceleration due to gravity and reach the ground simultaneously.Rate this question:
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- 38.
A person hold a bucket weigh 60 N. He walks 7 m along the horizontal and then climb up vertically 5 m. The work done by man is:
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A) 700 J
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B) 720 J
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C) 35 J
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D) 300 J
Correct Answer
A. D) 300 J -
- 39.
A stone, thrown at an angle to the horizontal in the gravitation field, follows a parabolic path PQRST in the absence of the air resistance. These points denote the position of the stone after successive equal time intervals. T is the highest point reached. The displaced PQ, QR, RS and ST:
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Has equal vertical components
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Increase at a constant rate
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has equal horizontal component
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Decrease at a constant rate
Correct Answer
A. has equal horizontal componentExplanation
The correct answer is that the displaced PQ, QR, RS, and ST have equal horizontal components. This means that the stone covers the same horizontal distance in each interval of time. Since the stone follows a parabolic path, its vertical component changes as it moves up and then down, but the horizontal component remains the same throughout its trajectory.Rate this question:
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- 40.
A mass of liquid of density p is mixed with an equal mass of another liquid of density is 3p. The density of liquid mixture is:
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A) p
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B) 3p
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C) 3p/2
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D) 3p/4
Correct Answer
A. C) 3p/2Explanation
When two liquids of different densities are mixed together in equal masses, the density of the resulting mixture can be found by taking the average of the two densities. In this case, the density of the first liquid is p, and the density of the second liquid is 3p. Taking the average of these two densities gives us (p + 3p)/2 = 4p/2 = 2p. Therefore, the density of the liquid mixture is 2p, which is equal to option C) 3p/2.Rate this question:
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- 41.
A girl stands on the weighing scale placed in a stationary elevator.The scale reads 30 kg. The elevator is then activated to move from ground floor to 10th floor. As the lift moves from its stationary position on the ground floor until it comes to rest on 10th floor. The scale reading during this passage :
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A) remains constant
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B) first increases, then remains constant for some particular time and then again tends to increase
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C) first increases, then remains constant for some particular time and then again tends to decrease
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D) first decreases, then remains constant for some particular time and then again tends to increase
Correct Answer
A. C) first increases, then remains constant for some particular time and then again tends to decreaseExplanation
As the elevator moves upwards, the girl experiences an increase in apparent weight due to the upward acceleration. This causes the scale reading to increase. Once the elevator reaches a constant velocity, the girl experiences a constant apparent weight and the scale reading remains constant. Finally, as the elevator decelerates to come to a stop on the 10th floor, the girl experiences a decrease in apparent weight, causing the scale reading to decrease. Therefore, the correct answer is C) first increases, then remains constant for some particular time and then again tends to decrease.Rate this question:
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- 42.
A stone tied to one end of the string is revolved around a rod in such a way that the string winds over the rod and get shortened. In this process, which of the following quantities remains same?
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A) Moment of Inertia
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B) Momentum
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C) K.E
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D) Angular momentum
Correct Answer
A. D) Angular momentumExplanation
When a stone tied to a string is revolved around a rod and the string winds over the rod and gets shortened, the distance between the stone and the rod decreases. However, the angular momentum of the stone remains the same. Angular momentum is the product of the moment of inertia and the angular velocity, and since the moment of inertia remains constant in this scenario, the angular momentum also remains constant. Therefore, option D) Angular momentum is the correct answer.Rate this question:
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- 43.
A solid sphere, a hollow sphere, a cylinder and a ring of the same radius are allowed to roll down from the same height. Assuming their masses to be equal which will reach last:
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A) Cylinder
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B) ring
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C) Solid sphere
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D) Hollow sphere
Correct Answer
A. B) ringExplanation
The ring will reach last because it has the least moment of inertia compared to the other objects. Moment of inertia is a measure of an object's resistance to changes in its rotation. The ring has all of its mass concentrated at the outer edge, resulting in a smaller moment of inertia. This allows it to rotate more easily and reach the bottom last compared to the other objects which have their mass distributed differently.Rate this question:
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- 44.
If the earth shrinks to half of its radius without changing in mass. the duration of the day will be:
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A) 12 hrs
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B) 48 hrs
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C) 24 hrs
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D) 6 hrs
Correct Answer
A. D) 6 hrsExplanation
If the earth shrinks to half of its radius, the distance from the center of the earth to any point on its surface will also be halved. This means that the circumference of the earth will also be halved. As the earth rotates once every 24 hours, if its circumference is halved, it will take half the time to complete one rotation. Therefore, the duration of the day will be 6 hours.Rate this question:
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- 45.
Water stands at Level B in the capillary tube as shown in the figure. If a jet of air is blown in the horizontal tube, then:
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A) Water level will rise above B
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B) Water level will fall below B
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C) There will no effect on the water flow
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D) Water will emerge from end A in the form of bubbles
Correct Answer
A. A) Water level will rise above BExplanation
When a jet of air is blown in the horizontal tube, it creates a decrease in pressure. This decrease in pressure will cause the water level in the capillary tube to rise above point B. This is because the decrease in pressure allows the atmospheric pressure to push the water up the tube, causing it to rise above its initial level.Rate this question:
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- 46.
Two light balls are suspended as shown in the figure. When a stream of air passes through the space between them, the distance between the balls will:
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Increase
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Decrease
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First increase then decrease
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Remains same
Correct Answer
A. DecreaseExplanation
When a stream of air passes through the space between the two light balls, it creates a force called the Bernoulli effect. This effect causes the air pressure between the balls to decrease, while the air pressure outside remains the same. As a result, the higher air pressure outside pushes the balls closer together, causing the distance between them to decrease. Therefore, the correct answer is "Decrease".Rate this question:
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- 47.
A mass spring system executing Simple harmonic motion. Then for what displacement, the P.E becomes 1/4 of its maximum value? Here, xo is taken as amplitude and x be displacement
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A) x=xo
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B) x=xo/2
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C) x=xo/4
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D) x=
Correct Answer
A. B) x=xo/2Explanation
The potential energy (P.E) of a mass-spring system in simple harmonic motion is given by the equation P.E = (1/2)kx^2, where k is the spring constant and x is the displacement from the equilibrium position. The maximum value of P.E occurs when x is equal to the amplitude (xo).
To find the displacement at which the P.E becomes 1/4 of its maximum value, we can set up the equation (1/4)P.E = (1/2)kx^2 and solve for x. By rearranging the equation, we get x^2 = (1/4)(2P.E/k). Simplifying further, x^2 = (1/2)(P.E/k). Taking the square root of both sides, we get x = sqrt((1/2)(P.E/k)).
Since P.E is proportional to x^2, when P.E is 1/4 of its maximum value, x will be sqrt((1/2)(1/4)), which simplifies to xo/2. Therefore, the correct answer is B) x = xo/2.Rate this question:
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- 48.
A simple pendulum suspended from the ceiling of a train has a period of T when the train is at rest.If the train starts moving with a constant acceleration, then the time period of pendulum:
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A) increases
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B) remains same
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C) decreases
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D) first decreases then remains constant
Correct Answer
A. C) decreasesExplanation
When the train starts moving with a constant acceleration, the pendulum experiences an additional force due to the acceleration. This force affects the effective length of the pendulum, causing it to decrease. As the length decreases, the time period of the pendulum also decreases. Therefore, the correct answer is C) decreases.Rate this question:
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- 49.
The frequency of the fundamental mode of the transverse vibration of a stretched wire is 1000 mm long is 250 Hz. When the wire is shortened to 500 mm at the same tension. What is the fundamental frequency?
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A) 125 Hz
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B) 500 Hz
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C) 250 Hz
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D) 1000 Hz
Correct Answer
A. B) 500 HzExplanation
When the wire is shortened to 500 mm while maintaining the same tension, the fundamental frequency of the transverse vibration will double. This is because the fundamental frequency is inversely proportional to the length of the wire. Therefore, if the length is halved, the frequency will double. In this case, the original frequency of 250 Hz becomes 500 Hz when the wire is shortened to 500 mm. Therefore, the correct answer is B) 500 Hz.Rate this question:
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Jul 04, 2024Quiz Edited by
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Jul 09, 2018Quiz Created by
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