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Q.

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)

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a

$4.4 \times {10^9}kg$

b

$7.6 \times {10^{14}}kg$

c

$3.8 \times {10^{12}}kg$

d

$3.8 \times {10^{14}}kg$

answer is D.

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Detailed Solution

$Energy\,\,rediated = 1.4\;kW/{m^2}$

$= 1.4\;kJ/\sec \;{m^2} = \frac{{1.4\;kJ}}{{\frac{1}{{86400}}day\;{m^2}}} = \frac{{1.4 \times 86400}}{{day\;{m^2}}}$

Total energy radiated/day

$= \frac{{4\pi \times {(1.5 \times {10}^{11})^2} \times 1.4 \times 86400}}{1}\frac{{kJ}}{{day}} = E$

$\therefore E = m{c^2} \Rightarrow m = \frac{E}{{{c^2}}}$

$= \frac{{4\pi (1.5 \times {10}^{11})^2} \times 1.4 \times 86400}{(3 \times {10}^8)^2} = 3.8 \times {10^{14}}kg$

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