A solid sphere, a hollow sphere, and a disc, all sharing identical mass and radius, are positioned at the top of an incline and released. The friction coefficients between the objects and the incline are identical and are insufficient to permit pure rolling. The minimum time to reach the bottom will be taken by

Step-by-step solution

Since the friction is insufficient to permit pure rolling, all the objects will slip as they move down the incline. The kinetic friction acting on each object is f_k = mg . The equation of motion for the center of mass is given by mg - f_k = ma . Substituting the value of f_k , we get a = g( - ) . The linear acceleration a is independent of the shape, mass, radius, and moment of inertia of the objects. Since all objects are released from rest and travel the same distance along the incline with the same acceleration