A solid sphere, a hollow sphere, and a disc, all possessing identical mass and radius, are released from the top of a smooth incline. The least time to reach the bottom will be taken by

Step-by-step solution

Since the incline is smooth, there is no frictional force to provide the necessary torque for rolling. Therefore, all the objects will purely slide down the incline without rolling. The acceleration of any object sliding down a smooth incline of angle is given by a = g , which is independent of the mass, radius, and shape (moment of inertia) of the body. Since all objects start from rest, cover the same distance s , and have the same acceleration, the time taken t = 2s g will be the same for all of them.