A) \[1.25\text{ }kWh\]
B) \[1.25\times {{10}^{7}}kWh\]
C) \[0.25\text{ }kWh\]
D) \[1.25\times {{10}^{4}}kWh\]
Correct Answer: B
Solution :
From Einsteins mass-energy relation, we get \[\Delta E=\Delta m{{c}^{2}}\] where c is speed of light. Am the difference in mass. Given, \[\Delta m=0.5\text{ }g=0.5\times {{10}^{-3}}kg,\] \[c=(3\times {{10}^{8}})\text{ }m/s\] \[\therefore \] \[\Delta E=0.5\times {{10}^{-3}}\times {{(3\times {{10}^{8}})}^{2}}\] \[\Rightarrow \] \[\Delta E=0.5\times 9\times {{10}^{13}}J\] Also, \[1\text{ }kWh=36\times {{10}^{5}}J\] \[\therefore \] \[\Delta E=\frac{0.5\times 9\times {{10}^{13}}}{36\times {{10}^{5}}}kWh\] \[\Delta E=1.25\times {{10}^{7}}kWh\]
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