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A ball weighing 1.0 kg is tied to a string 15 cm long. Initially the ball is held in position such that the string is horizontal. The ball is now released. A nail N its situated vertically below the support at a distance L. The minimum value of L such that the string will be wound round the nail is

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15 cm

4 cm

9 cm

None of these

answer is C.

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Detailed Solution

Velocity of bob at C should be $\sqrt{5 g (R - L)}$

$\sqrt{5 g (R - L)} = \sqrt{2 gR}$

$5(R-L) = 2R$

3R = 5L

$L = \frac{3}{5} R = \frac{3}{5} \times 15 = 9 cm$

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