Question

A bullet of mass $2g$ is having a charge of $2\mu C$ . Through what potential difference must it be accelerated, starting from rest, to acquire a speed of $10m/s$?

• A. 5 kV
• B. 50 kV
• C. 5 V
• D. 50 V

Answer 1

Answer: (B)

Key Idea : When bullet of mass $m$ and charge $q$ is accelerated through potential difference of $V$ volt, then it attains a kinetic energy equal to $qV$.
Kinetic energy of bullet $=qV$
ie, $\frac{1}{2}m{v}^2=qV$
$\Rightarrow V=\frac{m{v}^2}{2q}$
Given, $m=2g=2\times 10^{-3}kg,v=10m/s$
$q=2\mu C=2\times 10^{-6}C$
Substituting the values in relation for $V$, we' obtain
$V=\frac{2\times 10^{-3}\times (10{)}^2}{2\times 2\times 10^{-6}}$
$=50\times 10^{3}V=50kV$