A mass, m, moves in a circle on a smooth horizontal plane with velocity, V0, at a radius, R0. 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?
1/2mv20
1/4mv20
2mv20
mv20
Solution:
Angular momentum L is conserved since there is no torque acting on the particle. ∴mv0R0=mv′R0/2 ⇒v′=2V0 KEfinal=1/2mv′2=2mV20