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

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9 : 5

5 : 4

7 : 6

9 : 8

answer is D.

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Detailed Solution

(43πR3ρ).S.(−dθdt)=e.σ.(4πR2)(θ4−θ04)⇒RC=−dθdt=3eσPSR(θ4−θ04)∴ Initially, Rc∝eρSR∴(Rc)A(Rc)B=(eAeB)(ρBρA)(SBSA)(RBRA)=12.3.32.12=98

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