A cart of mass M is tied to one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system is on a smooth horizontal surface. The man is at x = 0 and the car at x = 10 m. If the man pulls the cart by the rope, the man and the cart will meet at the point.

At any instant, a rolling body may be considered to be in pure rotation about an axis trough the point of contact. This axis is translating forward with speed .

ABC is a right angled triangular plate of uniform thickness. The sides are such that AB > BC as shown in figure. I₁ , I₂, I₃ are moments of inertia about AB, BC and AC respectively. Then which of the following relations is correct ?

The moment of inertia of a disc of mass M and radius R about a tangent to its rim in its plane is

A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved ?

A solid cylinder of mass M and radius R rolls down an inclined plane of height h without slipping. The speed of its centre of mass when it reaches the bottom is

A solid sphere and a hollow sphere are thrown horizontally from a cliff with equal velocities, respectively. Then which sphere reaches first on earth ?

If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by

A thin uniform circular ring is rolling down an inclined plane of inclination 30o without slipping. Its linear acceleration along the inclined plane will be :