Question

A bulb of power \(660\ \text{W}\) radiates uniformly in all directions. The pressure exerted by the radiation on a surface at a distance of \(5\ \text{m}\) is

• A. \(5\times10^{-8}\ \text{Pa}\)
• B. \(2\times10^{-9}\ \text{Pa}\)
• C. \(7\times10^{-9}\ \text{Pa}\)
• D. \(\dfrac{3}{\pi}\times10^{-8}\ \text{Pa}\)

Hint:

For a source radiating uniformly in all directions, \[ I=\frac{P}{4\pi r^2}. \] Radiation pressure on a perfectly absorbing surface is \[ p=\frac{I}{c}, \] while for a perfectly reflecting surface it is \[ p=\frac{2I}{c}. \]

Answer 1

The Correct Option is C

Step 1: Find the intensity at r = 5 m.
\[ I = \frac{P}{4\pi r^2} = \frac{660}{4\pi\times25} = \frac{660}{100\pi} = \frac{6.6}{\pi}\,\text{W m}^{-2} \]

Step 2: Compute radiation pressure.
For absorbed radiation, \( P_{rad} = I/c \): \[ P_{rad} = \frac{6.6/\pi}{3\times10^8} = \frac{6.6}{3\pi\times10^8} \approx 7\times10^{-9}\,\text{Pa} \] \[ \boxed{7\times10^{-9}\,\text{Pa}} \]