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Question:

An electron of mass Me, initially at rest, moves through a certain distance in a uniform electric field in time t1. A proton of mass Mp also initially at rest, takes time t2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio t2/t1 is nearly equal to:

1

√MeMp

√MpMe

1836

Solution:

The acceleration of electron under electric field E is
ae = F/Me = qE/Me
Similarly acceleration of proton under electric field =
ap = F/Mp = qE/Mp
Since the distance traveled by both is same, we can write
s = 1/2 aet1^2 = 1/2 apt2^2
⟹ t2/t1 = √(ae/ap) = √(Mp/Me)