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  4. 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 is situated vertically below the support at a distance L.What is the minimum value of L (in cm) such that the string will be wound round the nail? <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/7c8deecfcf7a093e9c82a11f2c7cf9d5-.png />

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Q. 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 $N$ is situated vertically below the support at a distance $L$.What is the minimum value of $L$ (in cm) such that the string will be wound round the nail?
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Work, Energy and Power

Solution:

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Velocity of bob at $C$should be$\sqrt{5 gR}$
$\sqrt{5g \left(R -L\right)} = \sqrt{2 gR}$
$5\left(R -L\right) = 2R$
$3 R = 5 L$
$ L = \frac{3}{5} R = \frac{3}{5} \times 15 = 9\, cm $