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 = A epsi sigma T^(4) t`
or ` (Q)/(t) prop AT^(4)`
`(Q)/(t) prop r^(2) T^(4) " " (because A = 4 pi r^(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`