Explanation

(a) The relation between kinetic energy(K)and momentum p is given by
$K = \frac{p^{2}}{2m}$
Given , $m_{1} = 1g = 1 \times 10^{- 3}kg = 0.001kg,$
$m_{2} = 4g = 4 \times 10^{- 3}kg = 0.004\ kg,$
$\therefore\ K_{1} = K_{2}$
ie , $\frac{p_{1}^{2}}{\ 2m_{1}} = \frac{p_{2}^{2}}{2m_{2}}$
or $\frac{p_{1}}{p_{2}} = \sqrt{\frac{m_{1}}{m_{2}}} = \sqrt{\frac{0.001}{0.004}} = \frac{1}{2}$