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Q.

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

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a

13

b

13

c

31

d

1/313

answer is D.

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Detailed Solution

mc(dθ/dt)=σT44πr2or                              (dθ/dt)∝r2/m        ...(1)Further,  m=(4/3)πr3  or  r∝m1/3    ...(2)From eqs. (1) and (2), (dθ/dt)∝1/m1/3∴ (dθ/dt)1(dθ/dt)2=m2m11/3=131/3
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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