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Two metallic spheres S1 and S2 are made of the same material and have identical surface finish. The mass of S1 is three times 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 the initial rate of cooling of S1 to that of S2 is
  1. 1/3
  2. (1/3)1/3
  3. 3/1
  4. 1/3


Solution

The correct option is B (1/3)1/3
Rate of cooling (R)=AϵσVρc(T4T40)
RAV
Given that, they are two metallic spheres 
V=43πr3
A=4πr2
R1r
As m=ρV ; we get rm1/3
R1m1/3
R1R2=(m2m1)1/3=(13)1/3  (m1=3m2)

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