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 then equal to

1

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({\frac{m_{e}}{m_{p}})}^{\frac{1}{2}}

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({\frac{m_{p}}{m_{e}})}^{\frac{1}{2}}

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\frac{m_{p}}{m_{e}}

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Solution

The correct option is B $({\frac{m_{e}}{m_{p}})}^{\frac{1}{2}}$
Mass of electron $= m_{e}$
time $= t_{1}$
A proton of mass $= m_{p}$
time taken $= t_{2}$
$\frac{1}{2} a_{e} t_{e}^{2} = x_{e}$
$\frac{1}{2} a_{p} t_{p}^{2} = x_{p}$
$\Rightarrow a_{c} t_{c}^{2} / a_{p} t_{p}^{2} = 1$
$\Rightarrow \frac{t_{e}^{2}}{t_{p}^{2}} = \frac{a_{p}}{a_{e}}$
or, $\frac{t_{c}}{t_{p}} = \sqrt{\frac{M}{m}} = \sqrt{\frac{m_{e}}{m_{p}}}$ [ $∵$ Newton 2nd law $F = m a$ $m α \frac{1}{a}$ $m a s s α \frac{1}{a c c e l e r a t i o n}$ )

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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