Question

Solid sphere, hollow sphere, solid cylinder and hollow cylinder of same mass and same radii simultaneously start rolling down from the top of an inclined plane. The body that takes longest time to reach the bottom is:

• A. Solid sphere
• B. Hollow sphere
• C. Solid cylinder
• D. Hollow cylinder

Answer 1

Answer: (D)

Hollow cylinder

$a=\frac{gsin\theta }{1+\frac{I}{{mR}^2}}$
$\therefore$ The body whose acceleration is minimum will taken longest time to reach the rotation.
The body which has maximum moment of inertia will be having minimum acceleration.
$\therefore$ Hollow cylinder has the minimum acceleration as its Moment of Inertia is maximum among the all given bodies.