Q. The depth from the surface of the earth of radius $R$ at which the acceleration due to gravity will be 75% of the value on the surface of the earth is
A) $R/4$
B) $R/2$
C) $3R/4$
D) $R/8$
Explanation
(a) At depth $d$ from the surface of the earth.
$g^{'} = g\left( 1 - \frac{d}{R} \right)$
Given, $g^{'} = \frac{75}{100}g = \frac{3}{4}g$
Then, $\frac{3g}{4} = g\left( 1 - \frac{d}{R} \right)$
On solving, $d = R/4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.