Question

The ratio of thermal capacities of two spheres A and B, if 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

• A. $1:6$
• B. $1:12$
• C. $1:3$
• D. $1:4$

Answer 1

The correct option is D $1:4$

For sphere A

$C_1=V_1\times 2\rho \times S$

$=>C_1=\frac{4}{3}\times \pi r^3\times 2\rho \times S$

$=>C_1=\frac{8}{3}\times \pi r^3\rho S$

For sphere B

$C_2=V_2\times \rho \times 3S$

$=>C_2=\frac{4}{3}\times \pi (2r{)}^3\times 2\rho \times 3S$

$=>C_2=\frac{32}{3}\times \pi r^3\rho S$

so the ratio of their thermal capacity

$=\frac{C_1}{C_2}$

$=\frac{1}{4}$

Hence the ratio is $1:4$