JEE Main: Units, Dimensions And Error Analysis Quiz!

1. The radius of a cylinder is 4.23 cm and the height of the cylinder is 3.87 cm. Calculate the maximum permissible error in the calculation of the volume of the cylinder.

0.36

0.73

0.18

0.56

Explanation

2. The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speed ω. Considering the relation to be K = kI^aω^b where k is a dimensionless constant. What will be the value of 'a' and 'b'.

A = 2, b = 1

A = 1, b = 1

A = 1, b = 2

A = -1, b = 1

Explanation

3. The error in measurement of the momentum of a particle is 10% and if the mass is known exactly, what will be the error in the measurement of kinetic energy?

20%

10%

5%

6%

Explanation

4. There were printing errors in a paper that contains the four different formulas for the displacement 'y' of a particle undergoing a certain periodic motion. Which of the following can be correct?

Y = a sin 2π t/T

Y = a sin vt

Y = (a/T) sin t/a

Y = (a2) (sin 2πt / T + cos 2πt / T)

Among the all options only option is dimensionally correct and that’s why ‘a’ will be the correct option.

Explanation

Among the all options only option is dimensionally correct and that’s why ‘a’ will be the correct option.

5. The velocity of an object varies with time and as expressed in the equation: v =Xt² + Yt + Z. If units of v and t are expressed in terms of SI units, which of the following options correctly specifies the units of X, Y, and Z?

For the equation v = Xt²+Yt+Z the units of the right-hand side should be equal to the units of left-hand side. Each and every term is added with each other so all the terms must have the units equal to units of velocity (i.e. m s^-1). So now, unit of X = m s^-3, Unit of Y = m s^-2 and unit of Z = m s^-1. Option ‘C’ is correct.

Explanation

For the equation v = Xt²+Yt+Z the units of the right-hand side should be equal to the units of left-hand side. Each and every term is added with each other so all the terms must have the units equal to units of velocity (i.e. m s^-1). So now, unit of X = m s^-3, Unit of Y = m s^-2 and unit of Z = m s^-1. Option ‘C’ is correct.

6. Consider 'C' (velocity of light), 'G' (Universal Gravitational Constant) and 'h' (Planck's Constant) as the fundamental units of measurements, then which of the following will be the new dimensions of mass?

Explanation

7. A cube has sides of length 1.7 X 10^-3m. Calculate its volume.

4.913 X 10-9 m3

4.91 X 10-9 m3

4.90 X 10-9 m3

4.9 X 10-9 m3

The volume of a cube = a³; where ‘a’ is the side of the cube

In the question a = 1.7 $cross times$ 10^-3; so the volume = (1.7 $cross times$ 10^-3)³ = 4.913 $cross times$ 10^-9

but the side of the cube is given as 1.7 $cross times$ 10^-3and we have to take care that the answer must be is in the same format as the side so the volume of the cube is = 4.913 $cross times$ 10^-9

Explanation

The volume of a cube = a³; where ‘a’ is the side of the cube

In the question a = 1.7 $cross times$ 10^-3; so the volume = (1.7 $cross times$ 10^-3)³ = 4.913 $cross times$ 10^-9

but the side of the cube is given as 1.7 $cross times$ 10^-3and we have to take care that the answer must be is in the same format as the side so the volume of the cube is = 4.913 $cross times$ 10^-9

8. The dimensional formula for a physical quantity is [M²L³T^-2] the measurements of M = 12.00, L = 15.00, T = 14.00, then what will be the maximum percentage error in the measurement of the physical quantity.

0.2 %

0.3 %

0.4 %

0.5 %

Explanation

9. The velocity of a transverse wave in a string is given by the formula

where T is the tension in the string and m is mass per unit length. If T=7.0 Kg, the mass of the string is 5.0 g and the length of the string is 2.000 m then what will be the percentage error in the measurement of velocity?

1.74

0.72

2.31

3.63

Explanation

10. The weight of a body in the air is W₁=12 ± 0.04 N and the weight of the body in water is W₂=10 ± 0.03 N. What will be the relative density with the maximum permissible error?

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6.00 ± 0.031%

6.00 ± 0.069%

6.00 ± 3.12%

6.00 ± 6. 9%

Explanation