There are two spherical balls A and B of the same material with same surface, but the diameter of A is half that of B . If A and B are heated to the same temperature and then allowed to cool, then

Options

A. rate of cooling of 'A' is same as that of 'B'
B. rate of cooling of 'A' is twice that of 'B'
C. rate of cooling of 'A' is half that of 'B'
D. rate of cooling of 'A' is four times that of 'B'

Answer

C

Explanation

Rate of cooling `R_f=(e_r sigma A(T^4-T_0^(4)))/(ms)`
`R_1 prop (A)/(m) prop (A)/V prop (1)/(r)`
`(R_(f_1))/(R_(f_2))=(r_2)/(r_1)=(1)/2 implies R_(f_2)=2R_(f_1)`