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An electron of mass m e , initially at rest, moves though a certain distance in a uniform electric field in time t 2 A proton of mass m p , aslo, initially at rest, takes time t 2­ to move though an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio t 2 / t 1 is nearly equal to (a) 1 (b) (m p / m e ) 1/2 (c) (m e / m p ) 1/2 (d) 1836

An electron of mass me, initially at rest, moves though a certain distance in a uniform electric field in time t2 A proton of mass mp, aslo, initially at rest, takes time t to move though an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio t2 / t1 is nearly equal to
 
(a) 1
(b) (mp / me)1/2
(c) (me / mp)1/2
(d) 1836

Grade:upto college level

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago

(b) Let the distance to be travelled be x, Let the strength of uniform electric field be E, For electron

u = 0, s = x, a = eE/me , t = t1 , S = ut + ½ eE/2e x t21

? x = ½ eE/2 me x t21 …..(i)

For proton

u = 0, s = x, a = eE/ mp , t = t2, S = ut + ½ at2

? x = ½ eE/2mp x t22 ……(ii)

From (i) and (ii)

t22 / t21 = mp/me ? t2/ t1 = [mp / me]1/2

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