Question

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector is increased by 8 times, the intensity will

• A. increase by 8 times
• B. increase by 64 times
• C. decrease by 4 times
• D. decrease by 8 times

Hint:

For point sources, intensity always follows the inverse square law.

Answer 1

The Correct Option is C

Step 1: Relation between volume and radius.
For a spherical detector, \[ V \propto r^3 \]
Step 2: Find change in radius.
If volume increases by 8 times, \[ r_{\text{new}} = 2r \]
Step 3: Use inverse square law of intensity.
\[ I \propto \frac{1}{r^2} \]
Step 4: Compare intensities.
\[ I_{\text{new}} = \frac{1}{(2r)^2} = \frac{1}{4r^2} \] Hence, intensity decreases by 4 times.