Question

A solid sphere and a hollow sphere of the same mass and of the same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be \( t_1 \) and \( t_2 \), respectively, then:

• A. \( t_1>t_2 \)
• B. \( t_1 = 2t_2 \)
• C. \( t_1 = t_2 \)
• D. \( t_1<t_2 \)

Hint:

When comparing rolling objects, recall that objects with less moment of inertia relative to their mass and radius will accelerate faster and reach the bottom of the incline in less time.

Answer 1

The Correct Option is D

The time taken by an object to roll down an incline depends on its moment of inertia. The solid sphere has a smaller moment of inertia compared to the hollow sphere, which allows it to accelerate more quickly and reach the bottom in less time. Using the equation for rolling motion, the time taken for the solid sphere to reach the bottom will be less than the time taken by the hollow sphere, as the solid sphere has a greater rotational inertia compared to the hollow one. 
Final Answer: \( t_1<t_2 \).