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 rate of heat conduction is given by H= d d t = k A l T Here, T is same for both conductors, so ratio of heat conduction, aligned H₁ H₂ &= A₁ l₁ l₂ A₂ &= d₁² l₁ l₂ d₂² ( A= d² 4 ) &= ( d₁ d₂ )² l₂ l₁ &= ( 1 2 )² 1 2 = 1 8 aligned