==> \(2h{\nu _0} = h{\nu _0} + \frac{1}{2}mv_1^2\)

==> \(h{\nu _0} = \frac{1}{2}mv_1^2\) ...\(..(i)\)

and \(5h{\nu _0} = h{\nu _0} + \frac{1}{2}mv_2^2\) ==> \(4h{\nu _0} = \frac{1}{2}mv_2^2\) ...\(..(ii)\)

Dividing equation \((ii)\) by \((i)\) \({\left( {\frac{{{v_2}}}{{{v_1}}}} \right)^2} = \frac{4}{1}\)

==> \({v_2} = 2{v_1} = 2 \times 4 \times {10^6} = 8 \times {10^6}m/s\)