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 respectively by A and B per second is,

Options

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

Answer

D

Explanation

Ratio of thermal currents `=I_(1)//I_(2)=((DeltaT)/(R_(1)))/((DeltaT)/(R_(2)))=(R_(2))/(R_(1))=((l/K(pi(2D)^(2))/4))/((2l)/(K(piD^(2))/4))=1/8`