Rotational Motion

The moment of inertia of a solid cylinder about its own axis is given by: Where is the mass and is the radius of the cylinder. For a hollow cylinder, the moment of inertia is: Given that the radii of the solid and hollow cylinders are in the ratio 2:1, the ratio of their moments of inertia will be: Thus, the ratio of their moments of inertia is .

The correct option is (B) :

The two persons are initially at diametrically opposite points on a rotating platform. As they move towards each other, their distance from the center of the platform decreases, which means the moment of inertia of the system decreases. The moment of inertia of a rotating system is given by the formula: Where is the mass of the person and is the distance from the center. As decreases, decreases. According to the law of conservation of angular momentum, when the moment of inertia decreases, the angular velocity must increase to keep the angular momentum constant. Therefore, the angular velocity increases and the moment of inertia decreases as the persons move towards each other.

The correct option is (D) : angular velocity increases and moment of inertia decreases

Step 1: The moment of inertia of a solid cylinder about its central axis is: Step 2: The radius of gyration is related to the moment of inertia by: Step 3: Equating both expressions: Step 4: Therefore, the correct answer is (C).