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If electron of mass $m_e$ moves through a certain distance in a uniform electric field in time $t_1$ and proton of mass $m_p$ moves same distance in time $t_2$ , the ratio $\large\frac{t_1}{t_2}$ will be :

$(A)\;1 \\ (B)\;\bigg(\frac{m_p}{m_e}\bigg)^{1/2} \\ (C)\; \bigg(\frac{m_e}{m_p}\bigg)^{1/2} \\ (D)\;none $

1 Answer

$F= qE$
acceleration $a=\large\frac{qE}{m}$
For electron,
$s= \large\frac{1}{2} \bigg(\frac{qE}{m_e}\bigg) t_1^2$
For proton,
$s= \large\frac{1}{2} \bigg(\frac{qE}{m_p}\bigg) t_2^2$
Dividing both equations ,
$\bigg(\large\frac{t_1}{t_2} \bigg)^2=\frac{m_e}{m_p}$
Hence C is the correct answer.
answered Jan 15, 2014 by meena.p

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