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 intially 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 :

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{\frac{M_{p}}{M_{e}}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{\frac{M_{e}}{M_{p}}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1836

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\sqrt{\frac{M_{p}}{M_{e}}}$
The acceleration of electron under electric field $E$ is $a_{e} = \frac{F}{M_{e}}$ $= \frac{q E}{M_{e}}$
Similarly acceleration of proton under electric field= $a_{p} = \frac{F}{M_{p}}$ $= \frac{q E}{M_{p}}$
Since the distance traveled by both is same, we can write
$s = \frac{1}{2} a_{e} t_{1}^{2} = \frac{1}{2} a_{p} t_{2}^{2}$

$⟹ \frac{t_{2}}{t_{1}} = \sqrt{\frac{a_{e}}{a_{p}}}$ $= \sqrt{\frac{M_{p}}{M_{e}}}$

Suggest Corrections

Similar questions

Q. 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

\frac{t_{2}}{t_{1}}

is nearly equal to

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 $\frac{t_{2}}{t_{1}}$ is nearly equal to