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**1. Homework Statement**

A solid sphere, a hollow sphere and a disc, all having the same mass and radius are placed at the top on an incline and released. The friction coefficients between objects and the incline are same and not sufficient to allow pure rolling. Least time will be taken in reaching bottom by? Which object will have the least kinetic energy on reaching the bottom?

**2. Homework Equations**

**3. The Attempt at a Solution**

Since the friction is same for all, their accelerations down the plane will be same. Hence time taken will be same for all.

This implies that velocities at the bottom should be same (since they start from rest and reach in same time). Therefore the Kinetic energies must be equal.

But the answer is 'the hollow sphere' (for the second part)

One more thing, suppose the objects are in pure rolling motion (friction is sufficient). Then in that case will the time taken to reach the bottom of incline be same for all?