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A nail is located at a certain distance vertically below the point of suspension of a simple pendulum. The pendulum bob is released from the position where the string makes an angle of $60^{0}$ from the vertical. Calculate the value of $x$ if distance of the nail from the point of suspension is $\frac{x}{10}$ such that the bob will just perform revolution with the nail as centre. Assume the length of pendulum to be 1m.

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Detailed Solution

Let $l$ be the length of the pendulum rod from the suspension point to the the centre of the bob.

Velocity at lowest point $m g l (1 - \cos 60^{0}) = \frac{1}{2} m v^{2}$ (from energy conservation)

$v = \sqrt{g l}$

For completing the loop $v = \sqrt{5 g (l - r)} = \sqrt{g} l$

$r = \frac{4}{5} m$

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