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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)
$4.4 \times {10^9}kg$
$7.6 \times {10^{14}}kg$
$3.8 \times {10^{12}}kg$
$3.8 \times {10^{14}}kg$
Solution
(d) 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$
$\therefore E = m{c^2} \Rightarrow m = \frac{E}{{{c^2}}}$
$ = \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$.
