Question

If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hand, then his
(A) kinetic energy will decrease
(B) Moment of inertia will decrease
(C) angular momentum will increase
(D) Angular velocity will remain constant

Answer 1

Hint: we can use the concept of angular momentum. It is given in the question that the person is sitting on the rotating stool, so rotation occurs due to the effect produced by stool, not by any type of external torque. So in the absence of external force, the angular momentum gained by the person becomes conserved. We know that the angular momentum is directly related to the momentum of inertia and angular city. By keeping the value of angular momentum constant, we can determine the correct answer.

Complete step by step solution:
The body acquires momentum when it moves with some velocity. If the motion of the body is in a circular path, then it will acquire angular momentum. The angular momentum varies under external force action because external force tends to increase the angular velocity. But if there is no external force applied on the body, then its angular momentum becomes conserved. The angular momentum is directly related to the momentum of inertia and angular velocity.
If a person is sitting on a rotating stool with his hands outstretched, it will gain some angular momentum, which is conserved. But due to the sitting position of the person, the angular velocity of the person varies. When a person is sitting on a rotating stool with his hands outstretched, the person's angular velocity is less, but if suddenly the person lowers his hand, the person's angular velocity increases. Here the external force is not acting, so angular momentum is conserved, and due to this, the increased value of angular velocity will decrease the momentum of inertia.
Therefore, if a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hand, then his moment of inertia will decrease

So, the correct answer is “Option B”.

Note:
Option (A) is incorrect because the kinetic energy of the person increases if angular velocity increases, option (C) is incorrect because angular momentum is conserved, and option (D) is incorrect because angular velocity will change if the person changes its sitting position.