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Q.

A mass m moves in a circle on a smooth horizontal plane with velocity V₀ at a radius R. The mass is attached to 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 K.E is

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a

$2 {mV}_{0}^{2}$

b

$\frac{1}{2} {mV}_{0}^{2}$

c

${mV}_{0}^{2}$

d

$\frac{1}{4} {mV}_{0}^{2}$

answer is A.

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Detailed Solution

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$mvr = {mV}^{'} r^{'}$

$V_{0} R_{0} = V [\frac{R_{0}}{2}] \Rightarrow V = 2 V_{0}$

$\frac{K_{0}}{K} = \frac{\frac{1}{2} {mV}_{0}^{2}}{1 / 2 {mV}^{2}}$

$K = 4 K_{0} = 2 {mV}_{0}^{2}$

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A mass m moves in a circle on a smooth horizontal plane with velocity V0 at a radius R. The mass is attached to 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 K.E is