A) 0.026 MeV
B) 0.051 MeV
C) 0.079 MeV
D) 0.105 MeV
Correct Answer: C
Solution :
According to Einsteins equation relation between rest energy and moving energy is \[E={{E}_{0}}{{\left( 1-\frac{{{v}^{2}}}{{{c}^{2}}} \right)}^{-1/2}}\] Given, \[v=0.5\,\,c\] \[\therefore \] \[E={{E}_{0}}{{\left( 1-\frac{{{(0.5c)}^{2}}}{{{c}^{2}}} \right)}^{-1/2}}\] \[E={{E}_{0}}{{(1-0.25)}^{-1/2}}\] \[=\frac{{{E}_{0}}}{\sqrt{0.75}}\] Change in energy\[\Delta E=E-{{E}_{0}}\] \[=\frac{{{E}_{0}}}{\sqrt{0.75}}-{{E}_{0}}\] \[={{E}_{0}}\left( \frac{1}{\sqrt{0.75}}-7 \right)\] \[=0.511\left( \frac{1}{\sqrt{0.75}}-1 \right)\] \[=0.079\,\,MeV\]
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