A point mass is tied to one end of a cord whose other end passes through a vertical hollow tube, caught in one hand. The point mass is being rotated in a horizontal circle of radius 2 m with a speed of 4 m/s. The cord is then pulled down so that the radius of the circle reduces to 1 m. Complete the ratio of kinetic energies under the final and initial states

(4)

Here the force on the point mass due to the cord is radial and hence the torque about the centre of rotation is zero. Therefore, the angular momentum must remain constant as the cord is shortened

Let  and  be the mass, linear velocity and angular velocity of the point mass, respectively, in the circle of radius Further let  and  be the linear and angular velocities, respectively, of the point mass in a circle of radius . Now,

Initial angular momentum= final angular momentum

and