Two charged particles of masses $m$ and $2m$ have charges $+2q$ and $+q$ respectively. They are kept in uniform electric field and allowed to move for some time. The ratio of their kinetic energies will be
Diffcult
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Accelerations of particles are
$a_{1}=\frac{2 q E}{m}$ and $a_{2}=\frac{q E}{2 m}$
Their final velocities after time $\mathrm{t},$
${\mathrm{v}=0+\mathrm{at}=\mathrm{at}} $
$\mathrm{v}_{1}=\frac{2 \mathrm{q} \mathrm{E}}{\mathrm{m}} \mathrm{t}$ and $\mathrm{v}_{2}=\frac{\mathrm{q} \mathrm{E}}{2 \mathrm{m}} \mathrm{t}$
Ratio of kinetic energy of the two particles
$\frac{\mathrm{K}_{1}}{\mathrm{K}_{2}}=\frac{\frac{1}{2} \mathrm{mv}_{1}^{2}}{\frac{1}{2} 2 \mathrm{mv}_{2}^{2}}=\frac{\mathrm{v}_{1}^{2}}{2 \mathrm{v}_{2}^{2}}=\frac{8}{1}$
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