An electron (mass `m_(e )`)falls through a distance d in a uniform electric field of magnitude E.
,
The direction of the field is reversed keeping its magnitudes unchanged, and a proton(mass `m_(p)`) falls through the same distance. If the times taken by the electrons and the protons to fall the distance d is `t_("electron")` and `t_("proton")` respectively, then the ratio `t_("electron")//t_("proton")`.

Options

A. equal
B. smaller
C. `10` times greater
D. `5` times greater

Answer

b

Explanation

In case-I:
`h= (1)/(2)a_(e )t_(1)^(2)= (1)/(2)((eE)/(m_(e )))t_(1)^(2)`
In case-II:
`h= (1)/(2)a_(p)t_(2)^(2)= (1)/(2)((eE)/(m_(p)))t_(2)^(2)`
From (i) and (ii)
`(t_(1)^(2))/(t_(2)^(2))=(m_(e))/(m_(p))` or `(t_(1))/(t_(2))= sqrt((m_(e))/(m_(p)))`
As `m_(e)lt lt m_(p)` , hence `t_(1) lt t_(2)`