The kinetic energy of a moving body of linear momentum P is doubled. The final momentum of the body will be

$k_1=k; p_1=p$

$\mathrm{K}.\mathrm{E} \mathrm{is} \mathrm{double}$d

$k_2=2k;p_2=?$

We have relation between $p\&k \mathrm{as} {\mathrm{p}}^2=2\mathrm{km}$

${p_1}^2=2k_{2}m ; {p_2}^2=2k_{2}m$

$p^2=2 km ; {p_2}^2=2\left(2k\right)m$

$\therefore {p_2}^2=4km=2{p_1}^2$

${p_2}^2=2{p_1}^2$

$\therefore P_2=\sqrt{2}{P}_1=\sqrt{2}P$