If the temperature of the sun were to increase form `T to 2T `and its radius from `R to 2R`, then the ratio of the radiant energy received on earth to what it was previously will be

Options

A. (a)`4`
B. (b)`16`
C. (c)`32`
D. (d)`64`

Answer

D

Explanation

According to Stefan's law, power radiated by a perfectly black body is `P = sigmaAT^(4). P= sigma4piR^(2)T^(4)`
`(P_(2))/(P_(1)) = ((R_(2))/(R_(1)))^(2) ((T_(2))/(T_(1)))^(4) implies P_(2) = 64P_(1)`