Explanation

(b) Using the relation $p = \frac{1}{3}\frac{mnv^{2}}{V}$ …(i)
and also $p^{'} = \frac{1}{3}\frac{\frac{m}{2}n(2v)^{2}}{V}$ …(ii)
Dividing Eq.(ii) by Eq. (i), we get
$\frac{p'}{p} = 2$
So, $p:p^{'} = 1:2$
The ratio of initial and final pressures is $1:2$.