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`

Explanation

`k_(1)=k_(2)=k`
`2d_(1)=d_(2)` `(l_(1))/(l_(2))=2impliesl_(1)=2l_(2)`
`DeltaT_(1)=DeltaT_(2)`
`(I_(1))/(I_(2))=((k_(1)ADeltaT_(1)))/(l_(1))((k_(2)ADeltaT_(2)))/(l_(2))`
`(I_(1))/(I_(2))=((d_(1))/(d_(2)))^(2)xx((l_(1))/(l_(2)))xx((1)/(2))^(2)xx((1)/(2))=(1)/(8)`