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 _________.

ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. I _AB – I _BC and I _CA are the moments of inertia of the plate about AB, BC and CA as axes respectively. Which one of the following relations is correct ?
                                

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be

A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the centre of mass

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 flywheel rotating about a fixed axis has a kinetic energy of 360J when its angular speed is 30 rad/s. The moment of inertia of the wheel about the axis of rotation is _______.

Consider a system of two particles having masses m₁ and m₂.  If the particle of mass m₁ is pushed towards the mass centre of particles through a distance  d, by  what distance  would the particles of mass m₂ move so as to keep the mass centre of the particles at the original position?

A wheel of bicycle is rollling without slipping on a level road. The velocity of the centre of mass is v_cm, then true statement is

In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance 1.12 x 10 ^-10 m. The distance of the centre of mass form the carbon atom is _____.

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