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

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

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 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

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 ?

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

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

Two racing cars of masses m and 4m are moving in circles of radii r and 2r respectively. If their speeds are such that each makes a complete circle in the same time. Then the ratio of the angular speeds of the first to the second car is

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 :

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