A proton and an $α -$ particle start from rest in a uniform electric field, then the ratio of times of flight to travel same distance in the field is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$1 : \sqrt{2}$

$2 : 1$

$\sqrt{5} : \sqrt{2}$

$\sqrt{3} : 1$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given data: A proton and an α- particle

Concept used: Electric fields and force

Detailed solution:

Let m₁ and m₂ be the mass of the proton and α- particle

q₁ and q₂ be the charge of the proton and α- particle

We know that force acting on the particle placed in the electric field is

$F = E q m a = q E a = (\frac{q}{m}) E$

From equations of motion, we have

$s = u t + \frac{1}{2} a t^{2}$

Since both particles starts from rest u=0

$s = \frac{1}{2} a t^{2} s_{1} = s_{2} \frac{1}{2} a_{1} t_{1}^{2} = \frac{1}{2} a_{2} t_{2}^{2} \frac{1}{2} (\frac{q_{1}}{m_{1}}) E t_{1}^{2} = \frac{1}{2} (\frac{q_{2}}{m_{2}}) E t_{2}^{2} \frac{q_{1}}{m_{1}} t_{1}^{2} = \frac{q_{2}}{m_{2}} t_{2}^{2}$