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From given option (i) r = r₀, l = 2l₀, R = 2l₀ / Kπ(2r₀)² = l₀ / 2Kπr₀². (ii) r = r₀, l = l₀, R = l₀ / Kπr₀² = l₀ / 4Kπr₀². (iii) r = r₀, l = 2l₀, R = 2l₀ / Kπr₀² = 2l₀ / Kπr₀². (iv) r = r₀, l = l₀, R = l₀ / Kπr₀² = l₀ / Kπr₀². Heat flow will be maximum when r is maximum and l is minimum.

1. Rate of heat flow is directly proportional to area.
2. Rate of heat flow is inversely proportional to length.
3. Heat flow will be maximum when r is maximum and l is minimum.
4. None of the above.

Correct answer: Heat flow will be maximum when r is maximum and l is minimum.

Solution

The rate of heat flow is directly proportional to the cross-sectional area (A) and inversely proportional to the length (l). Hence, heat flow will be maximum when the radius (r) is maximum (as A ∝ r²) and the length (l) is minimum.

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