Two solid spheres A and B made of the same material have radii `r_(A)` and `r_(B)` respectively . Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling . The ratio of the rate of change of temperature of A and B is

Options

A. `(r_(A))/(r_(B))`
B. `(r_(B))/(r_(A))`
C. `(r_(A)^(2))/(r_(B)^(2))`
D. `(r_(B)^(2))/(r_(A)^(2))`

Answer

B

Explanation

`((-dT)/dt)=(3P)/(Prc)(T^(4)-T_(0)^(4))= H(assume)`
`(H_(A))/(H_(B))=(r_(B))/(r_(A))`
thus the ratio of change of temperature of A and `B = (r_(B))/(r_(A))`