A solid homogenous sphere of mass M and radius R is moving on a rough horizontal surface, party rolling and party sliding during this kind of motion of the sphere

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 ?

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

Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing trough a point on its rim will be

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 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

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

If a fly wheel makes 120 rev/min, then its angular speed will be

A particle of mass M is revolving along a circle of radius R and another particle of mass m is revolving in a circle of radius r. If time periods of both particles are same, then the ratio of their angular velocities is