A mass m moves in a circle on a smooth horizontal plane with velocity v 0 at a radius R 0 . The mass is attached to a string which passes through a smooth hole in the plane as shown.

The tension in the string is increased gradually and finally m moves in a circle of radius R₀/2 . The final value of the kinetic energy is :-

\(2 mv_o^2\)

Angular momentum remains Constant because of the torque of tension is zero.

L_i = L_f

mv_oR = mv\(\frac{R}{2}\)

⇒ v = 2v_o

KE = \(\frac{1}{2}mv^2\)

     = \(2 mv_o^2\)