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. $v=\sqrt{\frac{kQq}{mR}\left(2-\sqrt{2}\right)}$
• B. $v=\sqrt{\frac{kQq}{2mR}\left(2-\sqrt{2}\right)}$
• C. $v=\sqrt{\frac{kQq}{mR}}$
• D. $v=\sqrt{\frac{kQq}{\sqrt{2}mR}\left(1-\sqrt{2}\right)}$

Answer 1

Answer: (A)

$U_i+K_i=U_f+K_f$
$\frac{kQq}{\sqrt{2}R}+\frac{1}{2}m{v}^2=\frac{kQq}{R}+O$
$\frac{1}{2}m{v}^2=\frac{kQq}{R}\left(1-\frac{1}{\sqrt{2}}\right)$
$v=\sqrt{\frac{2kQq}{mR}\left(1-\frac{1}{\sqrt{2}}\right)}$
$v=\sqrt{\frac{kQq}{mR}\left(2-\sqrt{2}\right)}$