c
દળ ક્ષતિ \(\Delta {\text{M}} = \left[ {{\text{(M}} + \Delta {\text{m) - }}\left( {\frac{{\text{M}}}{{\text{2}}} + \frac{M}{2}} \right)} \right]\)

\(=[M+ \Delta m - M] = \Delta m\)

ઉત્પન થતી  ઉર્જા  \(Q = \Delta M c^2 = \Delta m c^2\).........\((1)\)

વેગમાન સરક્ષણ નિયમ પરથી ,

\((M + \Delta m)\,{X_0} = \frac{M}{2} \times \,\mathop {{\upsilon _1}}\limits^ \to   + \frac{M}{2} \times \mathop {{\upsilon _2}}\limits^ \to   \)

\(\Rightarrow \,\mathop {{\upsilon _2}}\limits^ \to   =  - \mathop {{\upsilon _2}}\limits^ \to  \,\,\)

\(\therefore\) \({\upsilon _1} = {\upsilon _2}\)

\(Q = \frac{1}{2}\left( {\frac{M}{2}} \right)\,\upsilon _1^2 + \frac{1}{2}\left( {\frac{M}{2}} \right)\upsilon _2^2 - \frac{1}{2}(M + \Delta m) \times {(0)^2}\)

\( = \frac{M}{2}\,\,\,\upsilon _1^2\,\,\,\,(\because \,\,\,{\upsilon _1} = {\upsilon _2})\,\,\,.....(2)\)

સમીકરણ \(1\) અને \(2\) ને સરખાવતા,

\(\left( {\frac{M}{2}} \right)\,\upsilon _1^2 = \Delta m{c^2}\)

\(\therefore\) \(\upsilon _1^2 = \frac{{2\Delta m{c^2}}}{M}\)

\(\therefore\) \({\upsilon _1} = c\sqrt {\frac{{2\Delta m}}{M}} \)