Question

You are given two spheres of same material and radii $10\,cm$ and $20\, cm$. They are heated to the same temperature. They are placed in the same environment. The ratio of their rates of cooling will be

• A. 1:02
• B. 2:01
• C. 1:04
• D. 4:01

Answer 1

Answer: (B)

2:01

Answer 2

Intensity of radiations emitted will be same from both the spheres. Let it be $I$. Then heat emitted per second Q = $4pr^2I$ . If $\Delta\,\theta_1$, be the change in temperature, then $Q = m C\Delta\theta = \left(\frac{4}{3}\right)\pi r^{3}\rho c \Delta\theta i.e \Delta\theta = 3I/rpc$ $4\pi r^{2}I=\left(\frac{4}{3}\right)\pi r^{3}\rho c \Delta\theta = \frac{3I}{rpc}$ $\frac{\Delta\theta_{1}}{\Delta\theta_{2}}=\frac{r_{2}}{r_{1}}=\frac{2}{1}$