Two metallic spheres $$S1$$ and $$S2$$ are made of the same material and have got identical surface finish. The mass of $$S1$$ is thrice that of $$S2$$. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of initial rate of cooling of $$S1$$ to that of $$S2$$ is

Question

Infinity Learn · Accepted Answer

$$mc(d$$θ$$/dt)=$$σ$$T44$$$$π$$$$r2or$$                              (d$$θ$$/dt)∝$$r2/m$$        ...(1)Further$$,  $$m=(4/3)π$$r3$$  or  r∝$$m1/3$$    ...(2)From$$ eqs. $$(1) and (2), (d$$θ$$/dt)∝$$1/m1/3$$∴ $$(d$$θ$$/dt)1(d$$θ$$/dt)2=m2m11/3=131/3$$

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