Question

Three similar spheres of mass $m$ and radius $r$ are moving down along three inclined planes $A,B$ and $C$ of similar dimensions. Sphere on inclined plane $A$ falls freely, sphere on inclined plane $B$ rolls without slipping and sphere on inclined plane $C$ slides down then:

• A. velocities of all the spheres are same.
• B. velocities of sphere on $A$ and $C$ are same whereas that on $B$ is less.
• C. velocities of sphere on $A$ is least and that on $C$ is maximum.
• D. velocity of sphere on $A$ is maximum.

Answer 1

Answer: (B)

velocities of sphere on $A$ and $C$ are same whereas that on $B$ is less.

In sphere A and C all the potential energy is converted to translational kinetic energy, while in B the potential energy is converted into translational and rotational kinetic energy.

Hence velocity of A=C>B