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 xx 10^11` meters. The mass lost by the sun per day is.

Options

A. `4.4 xx 10^9 kg`
B. `7.6 xx 10^14 kg`
C. `3.8 xx 10^12 kg`
D. `3.8 xx 10^14 kg`

Answer

D

Explanation

(d) Energy radiated `= 1.4 kW//m^2`
`=1.4 kJ//sec m^2 = (1.4 kJ)/((1)/(86400) "day" m^2) = (1.4 xx 86400)/( "day" m^2)`
Total energy radiated/day
`=(4 pi(1.5 xx 10^11)^2 xx 1.4 xx 86400)/(1) (kJ)/("day") = E`
`:. E = mc^2 rArr m = ( E)/(c^2)`
`=(4 pi(1.5 xx 10^11)^2 xx 1.4 xx 86400)/((3 xx 10^8)^2) = 3.8 xx 10^14 kg`.