d
\(\,v'\,\, = \,\,\left( {\frac{{{m_A}\, - \,\,{m_B}}}{{{m_A}\, + \,\,{m_B}}}} \right)\,v\,\,;\,\,\,\,\,e\,\, = \,\,1\,\, = \,\,\frac{{1.6v\, - \,\,v'}}{{v\, - \,\,0}}\,\,\, \Rightarrow \,\,v'\, = \,\,0.6v\)

\( \Rightarrow \,\,0.6v\,\, = \,\,\left( {\frac{{{m_A}\, - \,\,{m_B}}}{{{m_A}\, + \,\,{m_B}}}} \right)\,v\,\, \Rightarrow \,\,\frac{3}{5}\,\, = \,\,\frac{{{m_A}\, - \,\,{m_B}}}{{{m_A}\, + \,\,{m_B}}}\,\, \Rightarrow \,\,3{m_A}\, + \,\,3{m_B}\, = \,\,5{m_A}\, - \,\,5{m_B}\)

\(2{m_A}\, = \,\,8{m_B}\,\, \Rightarrow \,\,\frac{{{m_A}}}{{{m_B}}}\,\, = \,\,4,\)

વિનિમય પામતી ઉર્જા \(\%\) માં \(\,\, = \,\,\left[ {{\text{1}}\,\,{\text{ - }}\,\,{{\left( {\frac{{{\text{v'}}}}{{\text{v}}}} \right)}^2}} \right]\,\, \times \,\,100\% \,\, = \,\,\left[ {1\,\, - \,\,{{\left( {\frac{{6v}}{v}} \right)}^2}} \right]\,\, \times \,\,100\% \,\, = \,\,64\% \)