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Q.

A small mass attached to a string rotates on frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will

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a

increase by a factor of 4

b

remain constant

c

increase by a factor of 2

d

decrease by a factor of 2

answer is C.

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Detailed Solution

:K·E·=L22I

The angular momentum L remains conserved about the centre.

That is, L = constant.

I=mr2

K.E.=L22mr2

 In 2 nd case, K·E·=L22mr'2

 But r'=r2

K.E'=L22 mr24=4 L22mr2K.E.'=4 K.E

∴ K.E. is increased by a factor of 4.

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