The diagram show 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 pane a charge ` +Q` has also been fixed as shown. The potential at the point ` P` due to ` +Q` is `V` . The velocity which the bead should projected from the point `P` so that it can complete a circle should be greater than .

Options

A. `sqrt((6qV)/(m))`
B. `sqrt((qV)/(m))`
C. `sqrt((3qV)/(m))`
D. None of these

Answer

A

Explanation

`V_(rho) = V = (kQ)/(4a)`
`V_(x) = (kQ)/(a)`
`(1)/(2) mv^(2) = (kQ)/(a) - (kQ)/(4a) = (3kQ)/(4a)`
`(1)/(2)mv^(2) = 3 [(kQ)/(4a)] q = 3Vq`
`v = sqrt((6qV)/(m))`