Waves

JEE Main level, single correct, medium

24 of 142

Question 24 of 142

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

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Answer: (C) decrease by 4 times

For a point source, intensity is given by I=P4πr2I = \frac{P}{4\pi r^2} where PP is power and rr is distance.
If the volume of the spherical detector increases by 8 times, then 43πrnew3=8⋅43πrold3\frac{4}{3}\pi r_{new}^3 = 8 \cdot \frac{4}{3}\pi r_{old}^3, giving rnew=2roldr_{new} = 2r_{old}.
The new intensity is Inew=P4π(2rold)2=14⋅P4πrold2=Iold4I_{new} = \frac{P}{4\pi (2r_{old})^2} = \frac{1}{4} \cdot \frac{P}{4\pi r_{old}^2} = \frac{I_{old}}{4}.
Therefore intensity decreases by 4 times.

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