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A solid copper sphere (density \( \rho \) and specific heat capacity c) of radius \( r \) at an initial temperature \( 200 K \) is suspended inside a chamber whose walls are at almost \( 0 K \). The time required (in \( \mu \mathrm{s} \) ) for the temperature of the sphere to drop to
\( \mathrm{P} \) \( 100 K \) is
[IIT-JEE 1991]
(a) \( \frac{72}{7} \frac{r \rho c}{\sigma} \)
(b) \( \frac{7}{72} \frac{r \rho c}{\sigma} \)
(c) \( \frac{27}{7} \frac{r \rho c}{\sigma} \)
(d) \( \frac{7}{27} \frac{r \rho c}{\sigma} \)
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