A) 0.026 MeV
B) 0.051 MeV
C) 0.079 MeV
D) 0.105 MeV
Correct Answer: C
Solution :
Mass in moving condition and rest mass are related as \[m=\frac{{{m}_{o}}}{\sqrt{\left( 1-\frac{{{v}_{2}}}{{{c}^{2}}} \right)}}\] or \[m{{c}^{2}}=\frac{{{m}_{o}}{{c}^{2}}}{\sqrt{1-\frac{{{v}^{2}}}{{{c}^{2}}}}}\] \[\Rightarrow \] \[E={{E}_{0}}{{\left( 1-\frac{{{v}^{2}}}{{{c}^{2}}} \right)}^{-1/2}}\] Given, \[v=0.5c\] \[\therefore \] \[E={{E}_{0}}{{\left( 1-\frac{0.25{{c}^{2}}}{{{c}^{2}}} \right)}^{-\frac{1}{2}}}\] \[={{E}_{0}}{{(0.75)}^{-1/2}}\] \[=\frac{{{E}_{0}}}{\sqrt{0.75}}\] \[\therefore \] Change in energy \[=E-{{E}_{0}}\] \[\Delta E=\frac{{{E}_{0}}}{\sqrt{0.75}}-{{E}_{0}}\] \[{{E}_{0}}\left( \frac{1-\sqrt{0.75}}{\sqrt{0.75}} \right)\] Given, \[{{E}_{0}}=0.511MeV\] \[\therefore \] \[\Delta E=0.511\times \left( \frac{1-0.5\sqrt{3}}{0.5\sqrt{3}} \right)\] \[=0.079MeV\]
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