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Two spheres of equal radius R have densities in the ratio 8: 1 and specific heats in the ratio 1: 4. If, by radiation, their rates of fall of temperature are equal, find the ratio of their rates of heat loss.

1. 2: 1
2. 1: 1
3. 8: 1
4. 1: 2

Correct answer: 2: 1

Solution

With equal R (equal volume) and equal dT/dt, the heat-loss rate ratio equals (rho1 c1)/(rho2 c2) = (8*1)/(1*4) = 2:1.

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