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(B) Heat capacity $H_C$ is defined as the product of mass $m$ and specific heat capacity $c$,i.e.,$H_C = m \cdot c$.Since both spheres are made of the

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$1 : 8$

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(B) Heat capacity $H_C$ is defined as the product of mass $m$ and specific heat capacity $c$,i.e.,$H_C = m \cdot c$.Since both spheres are made of the same material,their specific heat capacities $c$ are equal.Therefore,the heat capacity is directly proportional to the mass: $H_C \propto m$.Since $m = V \cdot \rho$ (where $V$ is volume and $\rho$ is density),and density $\rho$ is the same for both,we have $H_C \propto V$.The volume of a sphere is $V = \frac{4}{3} \pi r^3$,so $H_C \propto r^3$.Given the ratio of diameters $d_1 : d_2 = 1 : 2$,the ratio of radii $r_1 : r_2$ is also $1 : 2$.Thus,the ratio of heat capacities is $\frac{(H_C)_1}{(H_C)_2} = \left( \frac{r_1}{r_2} \right)^3 = \left( \frac{1}{2} \right)^3 = \frac{1}{8}$.

Two spheres are made of the same material and have a diameter ratio of $1 : 2$. The ratio of their heat capacities is equal to ......

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