A mass m moves in a circle on a smooth horizontal plane with velocity ν0 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 R02 . The final value of the kinetic energy is
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a
2mv02
b
12mv02
c
mv02
d
14mv02
answer is A.
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Detailed Solution
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))