Q. A solid sphere and a hollow sphere of the same mass and of 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) $t_1=t_2$
C) $t_1<t_2$
D) $t_1=2t_2$
Explanation
[Solution by Dr. Abubacker] $a=\frac{g\sin\theta}{1+k^2/R^2}$: solid sphere $\frac{g\sin\theta}{7/5}$, hollow sphere $\frac{g\sin\theta}{5/3}$. The solid sphere has the larger acceleration, so it reaches the bottom first: $t_1<t_2$. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.