Question

A solid sphere, a hollow sphere and a ring, all having equal mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are equal but not sufficient to allow pure rolling. The greatest kinetic energy at the bottom of the incline will be achieved by:

• A. The solid sphere
• B. The hollow sphere
• C. The ring
• D. All will achieve same kinetic energy.

Answer 1

The correct option is B The hollow sphere

Assume each object has the same mass and the same outside diameter.

The moment of inertia of object.

Solid Sphere: $I_C=\frac{2m{R}^2}{5}$

Solid Cylinder:$I_C=\frac{m{R}^2}{2}$

Thin walled Hollow Sphere: $I_C=\frac{2m{R}^2}{3}$

Since,$KE=\frac{1}{2}{\omega }^{2}I$

hence, Hollow sphere has maximum kinetic energy.