Three particles  ${\mathrm{H}}^{+},{\mathrm{He}}^{+}\text{and }{\mathrm{Li}}^{++}$   are allowed to move from rest through the same potential difference. If  $v_A,v_B\text{ and }{v}_C$ are the velocities acquired as they emerge from the field region, then  $v_A:v_B:v_C$ equals : 

A particle of mass $m$ and charge $q$ moving through a potential difference $V$ acquires a velocity $v$ given by

$\begin{array}{l}\frac{1}{2}m{v}^2=qV\\ \Rightarrow v\propto \sqrt{\frac{q}{m}}\text{ if }V\text{ is the same }\end{array}$

For the particles  ${ }_{+1}^{1}H,{ }_{+1}^{4}He,{ }_{+2}^{6}L$ the ratio  $\mathrm{q}/\mathrm{m}$ is in

the ratio $1:\frac{1}{4}:\frac{1}{3}$. Hence, we have  

$v_A:v_B:v_C=1:\frac{1}{2}:\frac{1}{\sqrt{3}}=2\sqrt{3}:\sqrt{3}:2$.