Two copper spheres of radii 6 cm and 12 cm, respectively, are suspende

1.	Two copper spheres of radii 6 cm and 12 cm, respectively, are suspended in an evacuated enclosure. Each of them is at a temperature of 15 °C above the surroundings. The ratio of their rate of loss of heat is (A) 2 : 1 (B) 1 : 4 (C) 1 : 8 (D) 8 : 1.
Answer» Correct Option is (B) 1 : 4 Given, \(r_1 = 6 \ cm\) \(r_2 = 12 \ cm\) Rate of heat loss \(\theta = \sigma AT^4\) \(\theta_1 \propto A_1\) \(\because A = 4 \pi r^2\) \(\frac{\theta_1}{\theta_2} = \frac{4 \pi r_1 {^2}}{4 \pi r_2 {^2}}\) \(\frac{\theta_1}{\theta_2} = \left(\frac{r_1}{r_2}\right)^2\) \(\frac{\theta_1}{\theta_2} = \left(\frac{6}{12}\right)^2\) \(\theta_1 : \theta_2 = 1 : 4\) Correct option is (B) 1 : 4

Two copper spheres of radii 6 cm and 12 cm, respectively, are suspended in an evacuated enclosure. Each of them is at a temperature of 15 °C above the surroundings. The ratio of their rate of loss of heat is (A) 2 : 1 (B) 1 : 4 (C) 1 : 8 (D) 8 : 1.

Answer»

Correct Option is (B) 1 : 4

Given,

\(r_1 = 6 \ cm\)

\(r_2 = 12 \ cm\)

Rate of heat loss \(\theta = \sigma AT^4\)

\(\theta_1 \propto A_1\)

\(\because A = 4 \pi r^2\)

\(\frac{\theta_1}{\theta_2} = \frac{4 \pi r_1 {^2}}{4 \pi r_2 {^2}}\)

\(\frac{\theta_1}{\theta_2} = \left(\frac{r_1}{r_2}\right)^2\)

\(\frac{\theta_1}{\theta_2} = \left(\frac{6}{12}\right)^2\)

\(\theta_1 : \theta_2 = 1 : 4\)

Correct option is (B) 1 : 4