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A small sphere of mass m is connected by a string to a nail at O and moves in a circle of radius r on the smooth plane inclined at an angle $θ$ with the horizontal. If the sphere has a velocity u at the top position A. Minimum velocity at A so that string does not get slack instantaneously is

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$\sqrt{g r / 5}$

$\sqrt{3 g r}$

$\sqrt{2 g r / 5}$

$\sqrt{3 g r / 5}$

answer is A.

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Detailed Solution

$T_{A} + m g \sin 37^{0} = \frac{m v_{A}^{2}}{r}$ & $T_{A} \geq 0$

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