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Two spheres A and B have diameters in the ratio 1 : 2, densities in the ratio 2: I and specific heats in the ratio I : 3. Find the ratio of their thermal capacities.

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1 : 4

1 : 12

1 : 6

1 : 3

answer is B.

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Detailed Solution

$\frac{m_{A} C_{A}}{m_{B} C_{B}} = \frac{(\frac{4}{3}) {π_{A}}^{3} ρ_{A} C_{A}}{(\frac{4}{3}) {π_{B}}^{3} ρ_{B} C_{B}} = {(\frac{r_{A}}{r_{B}})}^{3} \frac{ρ_{A} C_{A}}{ρ_{B} C_{B}}$

= ${(\frac{1}{2})}^{3} \times (\frac{2}{1}) \times (\frac{1}{3}) = \frac{1}{12}$

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