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 $\frac{R_{0}}{2}$
The final value of the kinetic energy is

Question

Infinity Learn · Accepted Answer

Initial angular momentum Linitial $$=$$ $$mv0R0Initial$$ angular momentum Lfinal $$=$$ $$mvR02Conservation$$ of angular $$momentumm0v0R0$$ $$=$$ $$mvR02$$    ⇒ $$v=2v0KE$$ $$=$$ $$12mv2$$ $$=$$ $$2mv02$$

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