The heat is flowing through two cylinderical rods of same material. The diameters of the rods are in the ratio `1:2` and their lengths are in the ratio `2:1`. If the temperature difference between their ends is the same, the ratio of rates of flow of heat through them will be

Options

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

Answer

C

Explanation

(3) `(r_(1))/(r_(2)) = (1)/(2), (l_(1))/(l_(2)) = (2)/(1)`
`(i_(1))/(i_(2)) = (R_(2))/(R_(1)) = (l_(2))/(l_(1)). (r_(1)^(2))/(r_(2)^(2)) = (1)/(2) ((1)/(2))^(2) = (1)/(8)`