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. `(m_(p)// m_(e))^(1//2)`
C. `(m_(n) //m_(p))^(1//2)`
D. 1836

Answer

B

Explanation

Electrostatic force , `F_(e)=eE` (for both the particles)
But acceleration of electron, `a_(e)=F_(e)//m_(e)` and acceleration of proton, `a_(p)=F_(e)//m_(p)`
`S=(1)/(2)a_(e)t_(1)^(2)=(1)/(2)a_(p)t_(2)^(2)rArrtherefore(t_2)/(t_1)=sqrt((a_e)/(a_p))=sqrt((m_p)/(m_e))`