Question

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 plan. 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

• A. $\sqrt{\frac{6qV}{m}}$
• B. $\sqrt{\frac{qV}{m}}$
• C. $\sqrt{\frac{3qV}{m}}$
• D. $none$

Answer 1

The correct option is A $\sqrt{\frac{6qV}{m}}$

According to the question $i$ to complete full circle, Only minimum half circle completion is needed.

Apply Energy Comservation at point (1) , (2),

$\frac{1}{2}m{v}^2+\frac{kQq}{4a}=\frac{1}{2}m{v}_B^2+\frac{kQq}{a}$

also $V_B=0$ for minimum velocity of $V_A$

$\frac{1}{2}m{v}^2+qV=0+4Vq$

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

$v^{=}\sqrt{\frac{6qV}{m}}$

Hence,option $\text{A}$ is correct answer.