Question

The intensity at spherical surface due to an isotropic point source placed at its center is $I_0$. If its volume is increased by $8$ times, what will be intensity at the spherical surface? 

• A. Increase by $128$ times
• B. Increase by $8$ times
• C. Decrease by $4$ times
• D. Decrease by $8$ times

Hint:

For isotropic sources, intensity varies inversely as square of distance.

Answer 1

The Correct Option is C

Step 1: Relation between volume and radius.
\[ V \propto R^3 \Rightarrow 8V \Rightarrow R' = 2R \]
Step 2: Relation between intensity and radius.
\[ I \propto \dfrac{1}{R^2} \]
Step 3: Finding new intensity.
\[ I' = \dfrac{I_0}{(2)^2} = \dfrac{I_0}{4} \]