devarshi-dt-logo

Question:

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