Two conductors of the same material have their diameters in the ratio 1:2 and their lengths in the ratio 2: 1 . If the temperature difference between their ends is the same, then the ratio of amounts of heat conducted per second through them will be

Step-by-step solution

The resistance of conductor or R l r^2 R= l A = l r^2 aligned R₁ R₂ & = l₁ l₂ r₂^2 r₁^2 & = 2 1 ( 2 1 )^2= 8 1 aligned Thermal potentials between the ends of the rods are same. So, heat conducted per second aligned & H= Q t 1 R & H₁ H₂ = R₂ R₁ = 1 8 =1: 8 aligned