A) \[\frac{1}{4}\]
B) \[\frac{1}{16}\]
C) \[\frac{1}{32}\]
D) \[\frac{1}{64}\]
Correct Answer: D
Solution :
Heat capacity \[H=ms=\frac{4}{3}\pi {{r}^{3}}\rho s\]. For same material, density p and specific heat s are same, so heat capacity \[H\propto {{r}^{3}}\] Hence, the ratio of heat capacities is\[\frac{{{H}_{1}}}{{{H}_{2}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}={{\left( \frac{1}{4} \right)}^{3}}=\frac{1}{64}\]
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