Two spherical bodies A and B of diameter $$d=0.0344mm$$ are heated to the same temperature and allowed to coal in the same ambient temperature. Ratio of emissivities of their surfaces is $$1$$ : $$2$$, ratio of their specific heats is $$2$$ : $$3$$, ratio of their radii is $$2$$ : $$1$$ and ratio of their densities is $$1$$ : $$3$$. Then ratio of their initial rate of cooling is

Question

Two spherical bodies A and B of diameter $$d=0.0344mm$$ are heated to the same temperature and allowed to coal in the same ambient temperature. Ratio of emissivities of their surfaces is $$1$$ : $$2$$, ratio of their specific heats is $$2$$ : $$3$$, ratio of their radii is $$2$$ : $$1$$ and ratio of their densities is $$1$$ : $$3$$. Then ratio of their initial rate of cooling is

Infinity Learn · Accepted Answer

(43$$$$π$$$$R3$$ρ$$).S.$$($$−dθ$$dt)=e$$.σ.(4$$$$π$$$$R2)($$θ$$4$$−θ$$04)⇒$$RC=$$−dθ$$dt=3e$$σ$$PSR($$θ$$4$$−θ$$04)$$∴ Initially, Rc∝eρSR∴$$(Rc)A(Rc)B=(eAeB)($$ρBρ$$A)(SBSA)(RBRA)=12.3.32.12=98$$

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