A small sphere of mass m is tied to one end of a string of length l. The other end of the string is attached to a fixed point O. The sphere is released from position A when the string is horizontal and the sphere starts moving in a vertical circle. When the string makes an angle of θ with horizontal, centripetal acceleration of the sphere is,

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2g sin θ

g cos θ

g sin θ

2gcos θ

answer is A.

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Detailed Solution

If V be the speed of the sphere at position B,

Then conserving energy, $\frac{1}{2} {mv}^{2} = mglsinθ$

$\Rightarrow \frac{v^{2}}{l} = 2 gsinθ$

$∴$ Centripetal acceleration at B,

$a_{n} = \frac{v^{2}}{l} = 2 gsinθ$

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