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A solid sphere of radius $R$ and a hollow sphere of inner radius $r$ and outer radius $R$ made of copper are heated to the same temperature and are allowed to cool in the same environment. Then, choose the $CORRECT$ statement
Hollow sphere cools faster
Solid sphere cools faster
Both the spheres attain room temperature at the same time
The rate of loss of heat of the solid sphere is twice that of the hollow sphere
Solution
Rate of loss of heat $=\frac{\mathrm{d} \mathrm{Q}}{\mathrm{dt}}=\sigma e \mathrm{A}\left(\theta^{4}-\theta_{\mathrm{s}}^{4}\right)$ is equal
$\left(\frac{\mathrm{d} \theta}{\mathrm{dt}}\right)=\frac{\sigma \mathrm{e} \mathrm{A}}{\mathrm{ms}}\left(\theta^{4}-\theta_{\mathrm{s}}^{4}\right)$
since mass of hollow sphere is less its $\frac{\mathrm{d} \theta}{\mathrm{dt}}$ is more
Hollow sphere. Cools faster
