Question

A solid sphere, a hollow sphere and a disc having same mass and radius roll down the same inclined plane from rest. Which one will reach the ground in least time?

• A. Solid sphere
• B. Hollow sphere
• C. Disc
• D. All will reach in same time

Answer 1

Answer: (A)

The acceleration of a body rolling down an inclined plane is
$a=\frac{g \sin \theta}{\left(1+I / M r^{2}\right)}$
For solid sphere,
$I=\frac{2}{5} M R^{2}$
$\therefore a=\frac{5}{7} g \sin \theta$
For hollow sphere,
$I=\frac{2}{3} M R^{2}$
$\therefore a=\frac{3}{5} g \sin \theta$
For disc, $I=\frac{1}{2} M R^{2}$
$\therefore a=\frac{2}{3} g \sin \theta$
Acceleration is maximum for solid sphere hence, the solid sphere will reach the bottom in the least time.