The sphere of radii 8 cm and 2 cm are cooling. Their temperatures are `127^(@)C` and `527^(@)C` respectively . Find the ratio of energy radiated by them in the same time

Options

A. 0.06
B. 0.5
C. 1
D. 2

Answer

C

Explanation

Total energy radiated from a body
`Q=AepsilonsigmaT^(4)t" or " (Q)/(T)propAT^(4)rArr(Q)/(t)propr^(2)T^(4)" " (becauseA=4pir^(2))`
`therefore" " (Q_(1))/(Q_(2))=((r_(1))/(r_(2)))^(2)((T_(1))/(T_(2)))^(4)=((8)/(2))^(2)[(273+127)/(273+527)]^(4)=1`