Question

Two spheres made of same substance have diameters in the ratio 1 : 2. Their thermal capacities are in the ratio of

• A. 1:2
• B. 1:8
• C. 1:4
• D. 1:4

Answer 1

The correct option is B

1:8

Thermal capacity = Mass ´ Specific heat
Due to same material both spheres will have same specific heat. Also mass =
Volume (V) ´ Density (r)
\ Ratio of thermal capacity
=$\frac{m_1}{m_2}=\frac{V_1\rho }{V_2\rho }=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi R_2^3}=(\frac{r_1}{r_2}{)}^3=(\frac{1}{2}{)}^3=1:8$