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(B) The thermal capacity $C$ of an object is defined as the product of its mass $m$ and its specific heat capacity $S$,given by $C = mS$.Since the sph

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$1: 8$

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(B) The thermal capacity $C$ of an object is defined as the product of its mass $m$ and its specific heat capacity $S$,given by $C = mS$.Since the spheres are made of the same substance,they have the same density $ho$ and the same specific heat capacity $S$.The mass of a sphere is given by $m = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi r^3 ho$.Therefore,the thermal capacity is $C = \left( \frac{4}{3} \pi r^3 ho ight) S$.Since $\frac{4}{3}$,$\pi$,$ho$,and $S$ are constants,the thermal capacity is proportional to the cube of the radius,$C \propto r^3$.Given the ratio of diameters is $1: 2$,the ratio of radii $r_1 : r_2$ is also $1: 2$.The ratio of thermal capacities is $\frac{C_1}{C_2} = \left( \frac{r_1}{r_2} ight)^3 = \left( \frac{1}{2} ight)^3 = \frac{1}{8}$.Thus,the ratio is $1: 8$.

Two spheres made of the same substance have diameters in the ratio $1: 2$. Their thermal capacities are in the ratio of .............

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