d
આપણે જાણીએ છીયે કે \(, \,{{\text{v}}_{{\text{2f}}}}\,\, = \,\,\left( {\frac{{{{\text{m}}_{\text{2}}}\,\, - \,\,{m_1}}}{{{m_1}\,\, + \,\,{m_2}}}} \right)\,\,{{\text{v}}_{{\text{2f}}}}\,\, + \;\,\frac{{{\text{2}}{{\text{m}}_{\text{1}}}}}{{\left( {{{\text{m}}_{\text{1}}}\,\, + \,\,{m_2}} \right)}}\,\,{{\text{v}}_{{\text{1f}}}}{\text{ }}\)

\({{\text{m}}_{\text{1}}}\,\, = \,\,m,\,\,{m_2}\,\, = \,\,nm,\,\,{v_{1f}}\,\, = \,\,u,\,\,{v_{2f}}\,\, = \,\,0\,\,\, \Rightarrow \,\,{v_{2f}}\,\, = \,\,\frac{2}{{\left( {1\,\,\, + \;\,n} \right)}}\,\,u\)

અથડામણ બાદ સ્થિર કણ ની ગતિ ઉર્જા \(\, = \,\,\frac{1}{2}\,\,nm\,\,{\left[ {\frac{2}{{\left( {n\,\, + \;\,1} \right)}}\,\,u} \right]^2}\)

અથડામણ પહેલા m દળ ના કણ ની ગતિઉર્જા \( = \,\,\frac{{\text{1}}}{{\text{2}}}\,\,{\text{m}}{{\text{u}}^{\text{2}}}\)

તેથી વિનિમય પામતો ગતિ ઉર્જા નો અંશ \( = \,\,\frac{{\text{n}}}{{{{\text{u}}^{\text{2}}}}}\left[ {\frac{{{\text{4}}{{\text{u}}^{\text{2}}}}}{{{{\left( {n\,\, + \;\,1} \right)}^2}}}} \right]\,\, = \,\,\frac{{{\text{4n}}}}{{{{\left( {{\text{1}}\,\, + \;\,{\text{n}}} \right)}^2}}}\)