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Two spheres P and Q are made of the same good heat-conducting material, with the radius of Q three times that of P. When both are at the same surface temperature, the rate of fall of temperature of P is x times that of Q. Find x.

1. 1/4
2. 1/3
3. 3
4. 4

Correct answer: 3

Solution

Since dT/dt is proportional to surface area / mass, i.e. proportional to 1/r, the smaller sphere P cools 3 times faster than Q (r_Q = 3 r_P), so x = 3.

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