A mass m moves in a circle on a smooth horizontal plane with velocity $ν_{0}$ 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 $\frac{R_{0}}{2}$ . The final value of the kinetic energy is

Question

A mass m moves in a circle on a smooth horizontal plane with velocity $ν_{0}$ 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 $\frac{R_{0}}{2}$ . The final value of the kinetic energy is

Infinity Learn · Accepted Answer

According to law of conservation of angular $$momentummvr=mv$$'r'                                                     . . . .(i)v0R0=vR02$$;$$v=2v0$$∴  $$K0K=12mv0212mv2=v0v2$$ or $$KK0=vv02=(2)2K=4K0=2mv02$$                      . . . .$$(using$$ $$(i))

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