An electron of mass `M_e`, initially at rest, moves through a certain distance in a uniform electric field in time `t_1`. A proton of mass `M_p` also initially at rest, takes time `t_2` to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio `t_2//t_1` is nearly equal to

Options

A. `1`
B. `sqrt((M_p)/(M_e))`
C. `sqrt(M_e/M_p)`
D. `1836`

Answer

B

Explanation

Let a be the acceleration of the particle accelerated in electric field. Then distance travelled in time t is, `S=1/2at^2` or `t=sqrt((2S)/(a))` or `tprop1/a`
[`:'` S is constant]
`t_2/t_1=sqrt(a_e/a_p)=sqrt((F_e//M_e)/(F_p//M_p))=sqrt(M_p/M_e)`
`[:' F_e=F_p=eE]`