Nuclear Physics And Radioactivity Question 48
Question: The sun radiates energy in all directions. The average radiations received on the earth surface from the sun is $ 1.4\ kilowatt/m^{2} $ .The average earth- sun distance is $ 1.5\times 10^{11}metres $ . The mass lost by the sun per day is (1 day = 86400 seconds) [MP PMT 1993, 2003]
Options:
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 $
Show Answer
Answer:
Correct Answer: D
Solution:
Energy radiated $ =1.4\ kW/m^{2} $ $ =1.4\ kJ/\sec \ m^{2}=\frac{1.4\ kJ}{\frac{1}{86400}day\ m^{2}}=\frac{1.4\times 86400}{day\ m^{2}} $ Total energy radiated/day $ =\frac{4\pi \times {{(1.5\times 10^{11})}^{2}}\times 1.4\times 86400}{1}\frac{kJ}{day}=E $
$ \therefore E=mc^{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 $ .
BETA
