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

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 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 ?

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 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.

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 ?

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

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

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