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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 passesthrough 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 R02The final value of the kinetic energy is

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a

mv20

b

14mv02

c

2 mv02

d

12mv02

answer is C.

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Detailed Solution

Initial angular momentum Linitial = mv0R0Initial angular momentum Lfinal = mvR02Conservation of angular momentumm0v0R0 = mvR02    ⇒ v=2v0KE = 12mv2 = 2mv02
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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 passesthrough 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 R02The final value of the kinetic energy is