Question

A solid sphere, a solid cylinder, a hollow sphere and a hollow cylinder (all of same mass) simultaneously start rolling down from top of an inclined plane. If $a$ is acceleration of their centre of mass then $a$ is:

• A. maximum for solid cylinder, minimum for hollow sphere.
• B. maximum for hollow cylinder, minimum for solid sphere.
• C. maximum for hollow sphere, minimum for solid cylinder.
• D. maximum for solid sphere, minimum for hollow cylinder.

Answer 1

The correct option is D maximum for solid sphere, minimum for hollow cylinder.

Moment of Inertie for solid sphere=$\frac{2}{5}M{R}^2$
for solid cylinder=$\frac{1}{2}M{R}^2$
for hollow sphere=$\frac{2}{3}M{R}^2$
for hollow cylinder=$M{R}^2$
Torque acting $\tau =I\alpha$
$\therefore \alpha \propto \frac{1}{I}$
$I$ for hollow cylinder is highest and solid sphere is lowest.
$\therefore$ acceleration for solid sphere is highest and is lowest for hollow sphere