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

Energy `= (1.4 xx 10^(3))/((1)/(86400) "day "m^(2))= 1.4 xx 86400 xx 10^(3) J//"day " m^(2)`
Total energy `= 4pi r^(2) xx 1.4 xx 86400 xx 10^(3)`
`= 4pi xx (1.5 xx 10^(11))^(2) xx 1.4 xx 86400` J/day
Now,`E= mc^(2)`
`rArr m= (4pi xx (1.5 xx 10^(11))^(2) xx 1.4 xx 86400 xx 10^(3))/((3 xx 10^(8))^(2))= 3.8 xx 10^(14)kg`