PhysicsAn α particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

An $α$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

A
$\sqrt{2 : 1}$
B
$2 \sqrt{2} : 1$
C
$4 \sqrt{2} : 1$
D
$8 : 1$

Solution:

The liner momenta given by

$p = \sqrt{2 m E} = \sqrt{2 m q V} (∵ E = q V)$

$\frac{p_{α}}{p_{p}} = \sqrt{\frac{m_{α} q_{α}}{m_{p} q_{p}}} = \sqrt{\frac{4 m_{p} .2 q_{p}}{m_{p} q_{p}}} = \sqrt{\frac{4}{1} \times \frac{2}{1}} = \frac{2 \sqrt{2}}{1}$