Question

A particle of mass $1 \, kg$ and charge $\frac{1}{3} \, μC$ is projected towards a non conducting fixed spherical shell having the same charge uniformly distributed on its surface. The minimum initial velocity $V_{0}$ of projection of particle required if the particle just grazes the shell is

• A. $\sqrt{\frac{2}{3}}ms^{- 1}$
• B. $2 \, \sqrt{\frac{2}{3}}ms^{- 1}$
• C. $\frac{2}{3}ms^{- 1}$
• D. $1ms^{- 1}$

Answer 1

Answer: (B)

From conservation of angular momentum,
$mv_{0}\frac{r}{2}=mvr \, \Rightarrow v=\frac{v_{0}}{2}$
From conservation of energy,
$\frac{1}{2} m v_0^2=\frac{1}{2} m v^2+\frac{1}{4 \pi \epsilon_0}\left(\frac{q^2}{r}\right)$
$v_{0}=\sqrt{\frac{8}{3}}ms^{- 1}$