Two cylindrical conductors A and b of same metallic material have their diameters in the ratio 1 : 2 and lengths in the ratio 2 : 1 . If the temperature difference between their ends is same , the ratio of heats conducted respectivelty by A and B per sec is

Options

A. `1 : 2`
B. `1 : 4`
C. `1 : 16`
D. `1 : 8`

Answer

D

Explanation

`Q_(conc) = (kA(T_(1) -T_(2)))/(l)`
`Q prop (A)/(l)`
` implies (Q_(1))/(Q) = ((d_(1))/(d_(2)))^(2) xx (l_(2))/(l_(1))`
` implies (Q_(1))/(Q_(2)) = ((1)/(2))^(2) xx ((1)/(2))`
` therefore Q_(1) : Q_(2) = 1 : 8`