Q. One goes from the centre of the earth to a distance two third the radius of the earth, where will the acceleration due to gravity be the greatest?
A) At the centre of the earth
B) At a height half the radius of the earth
C) At a height one-third the radius of the earth
D) At a height two-third the radius of the earth
Explanation
(d) The acceleration due to gravity at a depth $d$ inside the earth is
$g^{'} = g\left( 1 - \frac{d}{R} \right) = g\left( \frac{R - d}{R} \right) = g\frac{r}{R}$
where, $R - d = r =$ distance of a place from the centre of earth, therefore, $g^{'} \propto r$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.