A) \[4.4\times {{10}^{9}}\,kg\]
B) \[7.6\times {{10}^{14}}\,kg\]
C) \[3.8\times {{10}^{12}}\,kg\]
D) \[3.8\times {{10}^{14}}\,kg\]
Correct Answer: D
Solution :
[d] energy radiated \[=1.4KW/{{m}^{2}}\] \[=1.4KJ/\sec {{m}^{2}}=\frac{1.4kJ}{\frac{1}{86400}day\,{{m}^{2}}}=\frac{1.4\times 86400}{day\,{{m}^{2}}}\] Total energy radiated/day \[=\frac{4\pi \,{{(1.5\times {{10}^{11}})}^{2}}\times 1.4\times 86400}{I}\frac{kJ}{day}=E\] \[\therefore \] \[E=m{{c}^{2}}\Rightarrow m=\frac{E}{{{c}^{2}}}\] \[=\frac{4\pi {{(1.5\times {{10}^{11}})}^{2}}\times 1.4\times 86400}{{{(3\times {{10}^{8}})}^{2}}}=3.8\times {{10}^{14}}kg.\]
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