Question

Two particles of masses $m$ and $2m$ having same charges $q$ each are placed in a uniform electric field $E$ and allowed to move for the same time. Find the ratio of their kinetic energies.

Answer 1

Let $K_1$ and $K_2$ be the kinetic energies of masses m amd 2m respectively.
$⟹K_1=\frac{1}{2}m{v_1}^2$ and $K_2=\frac{1}{2}2m{v_2}^2$
$⟹K_1=\frac{1}{2}m(a_{1}t{)}^2$
$K_2=\frac{1}{2}2m(a_{2}t{)}^2$
$⟹\frac{K_1}{K_2}=\frac{\frac{1}{2}m(a_{1}t{)}^2}{\frac{1}{2}2m(a_{2}t{)}^2}$..............(i)
$a_1=\frac{qE}{m}$ and $a_2=\frac{qE}{2m}$
Putting values of $a_1$ and $a_2$ in (i) we get
$\frac{K_1}{K_2}=2$