A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?

• Angular velocity

• Moment of inertia

• Angular momentum

• Rotational Kinetic energy

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

• Raindrops will fall faster

• Walking on the ground would become more difficult

• 'g' on the Earth will not change

• Time period of a simple pendulum on the Earth would decrease

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to

• 3D/2

• D

• 5D/4

• 7D/5

Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

• W_C > W_B> W_A

• W_A > W_B > W_C

• W_A>W_C>W_B

• W_B>W_A>W_C

Which one of the following statements is incorrect?

• Rolling friction is smaller than sliding friction.

• Limiting value of static friction is directly proportional to normal reaction.

• Coefficient of sliding friction has dimensions of length.

• Frictional force opposes the relative motion.

A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be

• 0.5

• 0.25

• 0.4

• 0.8

A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and θ for the block to remain stationary on the wedge is

• 

• 

• a = g tan θ

• a = g cos θ

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\overrightarrow{E}$ . Due to the force q $\overrightarrow{E}$, its velocity increases from 0 to 6 m/s in one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively

• 2 m/s, 4 m/s

• 1 m/s, 3 m/s

• 1.5 m/s, 3 m/s

• 1 m/s, 3.5 m/s

The moment of the force, at (2, 0, 3) about the point (2,-2,2), is given by

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is

• 0.521 cm

• 0.525 cm

• 0.529 cm

• 0.053