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Two metallic spheres A and B of the same material and identical surface finish are heated to the same temperature and then left to cool in a cooler, thermally insulated room. The mass of A is four times that of B. Which statement(s) is/are correct?

1. The ratio of heat loss of A to that of B is 2^(4/3)
2. The ratio of heat loss of A to that of B is 2^(2/3)
3. The ratio of the initial rate of cooling of A to that of B is 2^(-2/3)
4. The ratio of the initial rate of cooling of A to that of B is 2^(-4/3)

Correct answer: The ratio of heat loss of A to that of B is 2^(4/3)

Solution

Heat-loss rate scales with surface area, giving A: B = 4^(2/3) = 2^(4/3); the cooling rate scales as area/mass, giving 2^(-2/3) (so both the 2^(4/3) heat-loss and 2^(-2/3) cooling statements are correct).

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