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

Ratio of diameters, d₁ d₂ = 1 2 Ratio of lengths, l₁ l₂ = 2 1 The rate of heat conduction is given by the formula, H= d Q d t =k A l T where, d Q is the amount of heat transferred in d t time, k is coefficient of heat conduction for a particular material. Since, T is same in both cases, the ratio is aligned H₁ H₂ &= A₁ l₂ A₂ l₁ H₁ H₂ &= d₁² l₂ d₂² l₁ = 1 4 1 2 R=1: 8 aligned