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A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature $120\ ^oC$ , then
Both the cube and the sphere cool down at the same rate
The cube cools down faster than the sphere
The sphere cools down faster than the cube
Whichever is having more mass will cool down faster
Solution
Rate of cooling of a body
$\mathrm{R}=\frac{\Delta \theta}{\mathrm{t}}=\frac{\mathrm{A} \varepsilon \sigma\left(\mathrm{T}^{4}-\mathrm{T}_{0}^{4}\right)}{\mathrm{mc}}$
$\Rightarrow \mathrm{R} \propto \frac{\mathrm{A}}{\mathrm{m}} \propto \frac{\text { Area }}{\text { Volume }}$
$\Rightarrow$ For the same surface area. $\mathrm{R} \propto \frac{1}{\text { Volume }}$
$\because$ Volume of cube $<$ volume of sphere
$\Rightarrow \mathrm{R}_{\text {cute }}>\mathrm{R}_{\text {Sphere }}$ i.e., cube, cools down with faster rate
