"Two metallic spheres" `S_(1) "& "S_(2) "area made of same material /The mass of" S_(1) "Is thrice that of" S_(2) "Both of the spere are heated to the same temp and placed in the same ambient .Ratio of initial rate of cooling of" S_(1) "to that of" S_(2)`

Options

A. `1/3`
B. `(1)/(sqrt(3))`
C. `(1)/((3)^(1//3))`
D. `(1)/(sqrt(3)^(2//3))`

Answer

3

Explanation

`R_(c)propto (A)/(mS)`
`R_(c) propto (4pir^(2))/((4)/(3)pir^(3)ds)`
`R_(c) propto (1)/(rds)`
`m_(1)=3 m_(2)`
`(4)/(3)pir_(1)^(3)d=(4)/(3)pi_(3)^(3)dx3`
`r_(1)=3^(1/3)r_(2)`
`R_(c) propto 1/r`
`(R_(C_(1)))/(R_(C_(2)))=(r_(2))/(r_(1))=(1)/(3^(1/3))`