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

The angular speed of an engine wheel making 90 rev/min is

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 ?
       

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.

The moment of inertia of a body about a given axis is 1.2 kg – m². Initially, the body is at rest, in order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/s² must be applied about that axis for a duration of 

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

A round disc of moment of inertia I₂ about its axis perpendicular to its plane and passing through its center is placed over another disc of moment of inertia I₁ rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is

A couple produces

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 .

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is