\({p_i} = \sqrt {\left[ {m{{\left( {2V} \right)}^2} \times m{{\left( {2V} \right)}^2}} \right]} \)

\( = \sqrt 2 m \times 2V\)

Final momentum of the system\( = 3mV\)

By the law of conservation of momentum 

\(2\sqrt 2 mv \times 3mV\)

\( \Rightarrow \frac{{2\sqrt 2 v}}{3} = {V_{combined}}\)

Loss in energy

\(\Delta E = \frac{1}{2}{m_1}V_1^2 + \frac{1}{2}{m_2}V_2^2 - \frac{1}{2}\left( {{m_1} + {m_2}} \right)V_{combined}^2\)

\(\Delta E = 3m{v^2} - \frac{4}{3}m{v^2} = \frac{5}{3}m{v^2} = 55.55\% \)

Percentage loss in energy during the collision \(=56\%\)