Question

The minimum velocity $v$ with which charge $q$ should be projected so that it manages to reach the centre of the ring starting from the position shown in figure is

• A. $v=\sqrt{\frac{k Q q}{m R} \left(2 - \sqrt{2}\right)}$
• B. $v=\sqrt{\frac{k Q q}{2 m R} \left(2 - \sqrt{2}\right)}$
• C. $v=\sqrt{\frac{k Q q}{m R}}$
• D. $v=\sqrt{\frac{k Q q}{\sqrt{2} m R} \left(1 - \sqrt{2}\right)}$

Answer 1

Answer: (A)

$U_{i}+K_{i}=U_{f}+K_{f}$
$\frac{k Q q}{\sqrt{2} R}+\frac{1}{2}m v^{2}=\frac{k Q q}{R}+O$
$\frac{1}{2}mv^{2}=\frac{k Q q}{R}\left(1 - \frac{1}{\sqrt{2}}\right)$
$v=\sqrt{\frac{2 k Q q}{m R} \left(1 - \frac{1}{\sqrt{2}}\right)}$
$v=\sqrt{\frac{k Q q}{m R} \left(2 - \sqrt{2}\right)}$