A particle of mass \( m\) moving in the \(x\) direction with speed \(2v\) is hit by another particle of mass \(2m\) moving in the \(y\) direction with speed \(v\). If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to .............. \(\%\)

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

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

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 \(=56\%\)