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A nail is located at a certain distance vertically below the point of suspension of a simple pendulum of length 1m. The pendulum is released from the horizontal position. If it rotates in a vertical circle with nail as centre, the distance of nail from point of suspension is

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0.8m

0.5 m

0.4 m

0.6 m

answer is B.

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Detailed Solution

$v_{max}$ to complete circle about nail $= \sqrt{5 g (l - d)} \to (1)$

Loss is PE = gain in KE

$mg l = \frac{1}{2} {mv}^{2}$

$v = \sqrt{2 g l} \to (2)$

$\sqrt{5 g (l - d)} = \sqrt{2 g l}$

$5 l - 5 d = 2 l$

$d = \frac{3 l}{5} = 0.61 = 0.6 m$

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