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. `4.4xx10^(9)kg`
B. `7.6xx10^(14)kg`
C. `3.8xx10^(12)kg`
D. `3.8xx10^(14)kg`

Answer

D

Explanation

(d) Energy radiated `= 14kW//m^(2)`
`=1.4kj//sm^(2)=(1.4kj)/((1)/(86400)"days "m^(2))=(1.4xx86400kj)/("days "m^(2))`
total energy radiated /days
`E=(4pi xx(1.5xx10^(11))^(2)xx1.4xx86400)/(1)(kj)/(day )=E`
`therefore ` we have ,E = `mc^(2)`
`implies m=(E)/(c^(2))=(4pi(1.5xx10^(11))^(2)xx1.4xx86400)/((3xx10^(8))^(2))xx10^(3)`
`=3.8xx10^(14)kg `