Question

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 $t_2 / t_1$ l is nearly equal to

• A. 1
• B. $(m_p/m_e)^{1/2}$
• C. $(m_e/m_p)^{1/2}$
• D. 1836

Answer 1

Answer: (B)

$(m_p/m_e)^{1/2}$

Answer 2

Electrostatic force, $F_E =eE$ (for both the particles)
But acceleration of electron, $a_e=F_E /m_e$ and
acceleration of proton, $a_p=F_E /m_p$
$S=\frac{1}{2}a_e t^2_1=\frac{1}{2}a_p t^2_2 \, \, \Rightarrow \, \, \therefore \frac{t_2}{t_1}=\sqrt{\frac{a_e}{a_p}}=\sqrt{\frac{m_p}{m_e}}$