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. 2:1

Answer 1

The correct option is B 1:8

Thermal capacity = Mass $\times$ Specific heat
Due to same material both spheres will have same specific heat
$\therefore Ratioofthermalcapacity=\frac{m_1}{m_2}=\frac{V_1\rho }{V_2\rho }=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}={\left(\frac{r_1}{r_2}\right)}^3={\left(\frac{1}{2}\right)}^3=1:8$