System of Particles and Rotational Motion Test - 2

The moment of inertia is directly proportional to the square of the distance of mass from the axis of rotation.

Therefore, we have;

I ∝ r²

As the tube filled with water is rotated, as a result of the centrifugal force the water gets collected at the end of the tube. The distance of the rotation axis is increased. Consequently, the moment of inertia of the tube also increases

According to the law of conservation of angular momentum if there is no external force acting on the object or the system of several object then the angular momentum id conserved. In other words, the angular momentum remains unchanged.

Therefore, no external torque is applied on the person sitting on the stool. The quantity will remain unchanged.

According to the conservation of energy, we see that potential energy which only depends on the height (mgh); changes into kinetic energy by the time the sphere reaches the bottom. Thus the work done in both the cases is same.

The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum occurs. Therefore, for a system to be conserved, the net external torque acting on the system must be zero

if the external torque is zero,

L = Iω = constant.

It is an example of conservation of angular momentum is seen in an ice skater executing a spin. She can increase her rate of spin by pulling in her arms and legs. When she does this, the rotational inertia decreases and the rotation rate increases in order to keep the angular momentum,

L = Iω constant. (I: rotational inertia, ω: angular velocity)

Thus option B is the correct answer.

In both the option A and C, the ice skater will extend her body, increasing the moment of inertia. And to conserve the angular momentum, the angular velocity of the skater will decrease.

Rolling motion may be regarded as a combination of both the rotational motion about an axis through its center of mass and translational motion of the center of mass.

When a body rolls down without slipping along an inclined plane of inclination θ, it rotates about a horizontal axis through its center of mass and also its center of mass moves. As it rolls down, it suffers loss in gravitational potential energy provided translational energy due to frictional force is convened into rotational energy. Friction is needed to cause the body to roll.