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Q.

Two metallic spheres P and Q are of same surface finish and same density. Weight of P is twice that of Q. Both spheres are heated to same temperature and are left in room to cool by radiation. The ratio of initial rate of cooling of P to that of Q is

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a

1:2

b

2:1

c

1:(2)1/3

d

(2)2/3:1

answer is C.

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Detailed Solution

Let the mass of Q be m.∴mass of P = 2mNow,  −m.s.dTdt=eσ.(4πR2)(T4−T04)⇒−dTdt=eσ.(4πR2)43πR3ρS(T4−T04)⇒−dTdt=3eσρS1R(T4−T04)∴−dTdt∝1RNow 43πRp3ρ=2×43πRQ3ρ⇒Rp=(2)1/3.RQ∴Initial rate of cooling of PInitial rate of cooling of Q=RQRP=1(2)1/3
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