Question

The diagram shows a small bead of mass m carrying charge $q.$ The bead 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 is can complete a circle should be greater than

• A. $\sqrt{\frac{6qV}{m}}$
• B. $4\sqrt{\frac{qV}{m}}$
• C. $\sqrt{\frac{3qV}{m}}$
• D. $\sqrt{\frac{7qV}{2m}}$

Answer 1

Answer: (A)

$\sqrt{\frac{6qV}{m}}$

Mass of particle $=m$

change on particle $=q$

Potential at P due to charge $Q=V$

Potential at O due to change $Q=4V$

for completing circle

KE of particle = change in PE

$\frac{1}{2}m{u}^2=4qV-qV$

$u^2=\frac{6qV}{m}$

$u=\sqrt{\frac{6qV}{m}}$