Two charged particles of charge `+2q` and `+q` have masses `m` and `2m` respectively. Then are kept in uniform electric field allowed to move for the same time. Find the ratio of their kinetic energies.

Options

A. `1:8`
B. `16:1`
C. `2:1`
D. `3:1`

Explanation

(b) Let `E=` uniform electric field
Let `m_(1)=m, m_(2)=2m`
Force on particles,
`F_(1)=ma_(1)=2qE`
`implies F_(2)=2ma_(2)=qE`
`a_(1)=(2qE)/m` and `a_(2)=(qE)/(2m)`
Final velocities of the particle
`v_(1)=u_(1)=a_(1)t`
`implies v_(1)=(2qE)/m timpliesv_(2)=(qE)/(2m)t`
Let `K=` kinetic energy
`K_(1)=1/2m ((qE)/(2m))^(2)t^(2)implies(K_(1))/(K_(2))=16/1`