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. 4
B. 16
C. 32
D. 64

Answer

D

Explanation

(4) `u = e sigma A T^(4) = e sigma 4 pi R^(2)T^(4)`
`u prop T^(2) T^(4)`
`u' prop (2 R)^(2) (2T)^(4)`
`(u')/(u) = 64`