Question

A solid sphere, a hollow sphere and a disc, all having the same mass and radeius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The least time will be taken in reaching the bottom by

• A. the solid sphere
• B. the hollow sphere
• C. the disc
• D. all will take the same time

Answer 1

The correct option is D all will take the same time

As the point A is sliding thus kinetic friction will act.

$f=\mu mgcos\theta$

$ma=mgsin\theta -\mu mgcos\theta ⟹a$ is same for all the bodies

Now , $s=0+\frac{1}{2}a{t}^2=\frac{1}{2}a{t}^2$ where s is the distance travelled by body on the inclined plane

Thus for same $s$ , all will take the same time.