Question

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

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

Answer 1

The correct option is D The hollow sphere

Diagram
Hence, angular momentum is also same.
$KE=\frac{1}{2}M{v}^2+\frac{L^2}{2I}$
Linear velocity ${}^{\prime }{v}^{\prime }$ is the same for all as the same force acts on them. Therefore, more value of moment of inertia implies lesser kinetic energy.
Order of the moment of inertia of the bodies:-hollow sphere > disc >solid sphere.
Hence, the hollow sphere will have the smallest kinetic energy at the bottom.