Question

A solid sphere and hollow sphere roll down purely equal distances on the same inclined plane (starting from rest) in time \( t_1 \) and \( t_2 \). Then

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

Hint:

In rolling motion, objects with a smaller moment of inertia (such as a solid sphere) roll down faster than objects with a larger moment of inertia (such as a hollow sphere).

Answer 1

The Correct Option is B

When both spheres roll down an incline starting from rest, they undergo pure rolling motion. For pure rolling motion, the time taken depends on the moment of inertia of the object. A solid sphere has a smaller moment of inertia compared to a hollow sphere, which causes it to accelerate faster and thus take less time to cover the same distance. Thus, the solid sphere reaches the bottom in less time than the hollow sphere, so \( t_1<t_2 \).