Question

Two spheres have their radii in the ratio 1 : 2, the densities of their materials are in the ratio 2 : 3 and their specific heats are in the ratio 3:4, then the ratio of their thermal capacities is

• A. 3 : 4
• B. 1 : 16
• C. 2 : 3
• D. 1 : 1

Answer 1

The correct option is B 1 : 16

Thermal capacity$=$mass$\times$specific heat.
Mass$=$volume$\times$density
For a sphere, volume is directly proportional to its cube of radius.
$\therefore TC\propto r^3.\rho .C$
$\Rightarrow \frac{T{C}_1}{T{C}_2}=\frac{{r_1}^3.{\rho }_1.C_1}{{r_2}^3.{\rho }_2.C_2}$
$\frac{T{C}_1}{T{C}_2}=(\frac{1}{2}{)}^3.(\frac{2}{3}).(\frac{3}{4})$
$\frac{T{C}_1}{T{C}_2}=\frac{1}{16}$
Option B.