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

Step-by-step solution

For a point source, intensity is given by I = P 4 r^2 where P is power and r is distance. If the volume of the spherical detector increases by 8 times, then 4 3 r_ new ^3 = 8 4 3 r_ old ^3 , giving r_ new = 2r_ old . The new intensity is I_ new = P 4 (2r_ old )^2 = 1 4 P 4 r_ old ^2 = I_ old 4 . Therefore intensity decreases by 4 times.