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

Answer

D

Explanation

`Q=(KA(theta_(1)-theta_(2)t))/(l)rArr(Q)/(t)=(Kpir^(2)(Deltatheta))/(l)`
`:.(((Q)/(t))_(1))/(((Q)/(t))_(2))=(K_(1))/(K_(2))xx((r_(1))/(r_(2)))^(2)`