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In a gymnast, sitting on a rotating stool, with his arms outstretched, suddenly lowers his arms
(A) The angular velocity decreases
(B) His moment of inertia decreases
(C) The angular velocity remains constant
(D) The angular momentum increases

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Last updated date: 20th Jun 2024
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Answer
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Hint It should be known to us that a body will always have a tendency to resist angular acceleration. This will be equal to the sum of the products of the mass of each of the particles in the body along with the square of its distance from the axis of the rotation. With the help of this concept we have to solve this question.

Complete step by step answer:
This answer is based on the concept of angular momentum. So, it is required for us to know to solve this question. This law will state that if we apply external force on an object, then only the momentum will change or else it will not.
To answer this question at first we have to analyse the situation that is mentioned in the question. So, it is known that, when the gymnast lowers his arms, the distribution of mass changes about the axis of rotation. As there is the mentioning of the rotation, it means that we have to consider the distribution of mass as well.
As we can see that the mass comes more near to the axis and thus the moment of inertia of the rotating system is reduced.
So, at first as it is mentioned, the law of conservation of momentum is fulfilled.

Hence, the correct answer is Option B.

Note From the concept of moment of inertia we can say that the calculation is required so as to know the force that is needed to rotate an object. The value can be manipulated to either to increment or the decrement. By increasing the radius from the axis of the rotation, the moment of inertia increases thus resulting in the slowing down of the speed of rotation.