The ratio of thermal capacities of two spheres A and B, their diameters are in the ratio `1:2` densities in the ratio `2:1`, and the specific heat in the ratio of `1:3`, will be

Options

A. `1:6`
B. `1:12`
C. `1:3`
D. `1:4`

Answer

B

Explanation

`(m_(A)c_(A))/(m_(B)c_(B)) = ((4//3)pi r_(A)^(3)rho_(A)c_(A))/((4//3)pi r_(B)^(3)rho_(B)c_(B)) = ((r_A)/(r_B))^(3) (rho_(A)c_(A))/(rho_(B)c_(B))`
`(m_(A)c_(A))/(m_(B)c_(B)) = (1/2)^(3) xx 2/1 xx (1/3) = 1/12` .