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(C) The acceleration $a$ of a particle of charge $q$ and mass $m$ in a uniform electric field $E$ is given by $a = \frac{qE}{m}$.Using the equation of

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$1: \sqrt{2}$

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(C) The acceleration $a$ of a particle of charge $q$ and mass $m$ in a uniform electric field $E$ is given by $a = \frac{qE}{m}$.Using the equation of motion $s = ut + \frac{1}{2}at^2$,since the particles start from rest $(u = 0)$,we have $s = \frac{1}{2}at^2$.Thus,$t = \sqrt{\frac{2s}{a}} = \sqrt{\frac{2sm}{qE}}$.For equal displacements $s$,the time $t$ is proportional to $\sqrt{\frac{m}{q}}$.Let $m_p$ and $q_p$ be the mass and charge of the proton,and $m_\alpha$ and $q_\alpha$ be the mass and charge of the alpha particle.We know $m_\alpha = 4m_p$ and $q_\alpha = 2q_p$.The ratio of times is $\frac{t_p}{t_\alpha} = \sqrt{\frac{m_p}{q_p} \cdot \frac{q_\alpha}{m_\alpha}} = \sqrt{\frac{m_p}{q_p} \cdot \frac{2q_p}{4m_p}} = \sqrt{\frac{2}{4}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$.

An alpha particle and a proton are accelerated from rest in a uniform electric field. The ratio of the times taken by proton and alpha particle to attain equal displacements is

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