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A small spherical ball is suspended through a string of length l. The whole arrangement is placed in a vehicle which is moving with velocity v. Now, suddenly the vehicle stops and ball starts moving along a circular path. If tension in the string at the highest point is twice the weight of the ball, then (Assume that the ball completes the vertical circle)

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$v = \sqrt{5 gl}$

$v = \sqrt{7 gl}$

the velocity of the ball at the highest point is $\sqrt{3 gl}$

velocity of the ball at highest point is $\sqrt{gl}$

answer is B, D.

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Detailed Solution

$T + mg = \frac{{mu}^{2}}{l}$

$∴ 2 mg + mg = \frac{{mu}^{2}}{l} or u = \sqrt{3 gl} v^{2} = u^{2} + 2 gh = 3 gl + 2 g (2 l) = 7 gl ∴ v = \sqrt{7 gl}$

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