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

As we use `Q=(kADeltatheta)/(l)=(k(pir^(2))Deltathetat)/(l)`
`implies (Q_(1))/(Q_(2))=(r_(1)^(2))/(l^(1))xx(l_(2))/(r^(2))=((1)/(2))^(2)xx((1)/(2))=(1)/(8)`