Two particles of mass `m` and `2m` with charges 2q and q are placed in a uniform electric field E and allowed to move for same time. Find the ratio of their kinetic energie

Options

A. `1:1`
B. `4:1`
C. `1:4`
D. `8:1`

Answer

D

Explanation

Accleration of particles are
`a _(1) = (2 qE)/(m) and a _(2) = (q E)/( 2m)`
Their final velocities after time t,
`v = 0 + at = at`
` v _(1) = (2q E)/(m )t and v _(2) = ( q E)/( 2m )t`
Ratio of kinetic energy of the two particles
`( K _(1))/(K _(2)) =((1)/(2) mv _(1) ^(2))/( (1)/(2) mv _(2) ^(2)) = (v _(1) ^(2))/(2 v _(2) ^(2)) = (8)/(1)`