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A sphere of density p, specific heat capacity c and radius r is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure and the nature of the surface of sphere and is proportional to:

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a

cr3ρ

b

1r3ρc

c

3r3pc

d

1rpc

answer is D.

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Detailed Solution

−dTdt=σAmcT−T0=σ4πr2ρ×43πr3cT−T0∴ −dTdt∝1ρrc

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A sphere of density p, specific heat capacity c and radius r is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure and the nature of the surface of sphere and is proportional to: