The diagram shows a small bead of mass m carrying charge q . The bead can freely move on the smooth fixed ring placed on a smooth horizontal plane. In the same plane a charge +Q has also been fixed as shown. The potential at the point P due to +Q is V. The velocity with which the bead should projected from the point P so that it can complete a circle should be greater than

\sqrt{\frac{6 q V}{m}}

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\sqrt{\frac{q V}{m}}

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\sqrt{\frac{3 q V}{m}}

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\sqrt{\frac{4 q V}{m}}

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Solution

The correct option is A $\sqrt{\frac{6 q V}{m}}$
Applying conservation of energy
$V . q + \frac{1}{2} m u^{2} = 4 V . q + 0 \Rightarrow u = \sqrt{\frac{6 V q}{m}}$

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