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Q.

A simple pendulum consists of a point mass $m$ attached to a light inextensible string of length $L$ . The pendulum is given as initial angular displacement of $60 °$ from the mean position and released from rest. During the period it moves from $60^{\circ} t o 30 °$ .

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a

work done by gravity is $\frac{m g L (\sqrt{3} - 1)}{4}$

b

work done by gravity is $\frac{m g L (\sqrt{3} - 1)}{2}$

c

work done by the string tension is $\frac{m g L (\sqrt{3} - 1)}{4}$

d

total work done by gravity and the string tension is $\frac{m g L (\sqrt{3} - 1)}{2}$

answer is C, D.

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Detailed Solution

$W_{g r a v i t y} = m g y = m g L (\cos 30^{\circ} - \cos 60^{\circ})$

$= \frac{m g L}{2} (\sqrt{3} - 1)$

$W_{T e n s i o n} = 0$

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A simple pendulum consists of a point mass m attached to a light inextensible string of length L. The pendulum is given as initial angular displacement of 60° from the mean position and released from rest. During the period it moves from 60∘ to 30°.