COMEDK · Physics · 12. Thermal Properties of Matter

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

A \(8: 1\)
B \(1: 8\)
C \(4: 1\)
D \(1: 4\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1: 8\)

Step-by-step Solution

Detailed explanation

Ratio of diameters, \(\frac{d_{1}}{d_{2}}=\frac{1}{2}\) Ratio of lengths, \(\frac{l_{1}}{l_{2}}=\frac{2}{1}\) The rate of heat conduction is given by the formula, \[ H=\frac{d Q}{d t}=k \frac{A}{l} \Delta T \] where, \(d Q\) is the amount of heat transferred in \(d t\) time,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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