Q. The ratio of acceleration due to gravity at a height $h$ above the surface of the earth and at a depth $h$ below the surface of the earth for $h < \ <$ radius of earth
A) Is constant
B) Increases linearly with $h$
C) Decreases linearly with $h$
D) Decreases parabolically with $h$
Explanation
(c) Acceleration due to gravity at height $h$,
$g_{1} = g\left( 1 - \frac{2h}{R} \right)$
Acceleration due to gravity at depth $h$,
$g_{1} = g\left( 1 - \frac{h}{R} \right)$
$\therefore\frac{g_{1}}{g_{2}} = \frac{1 - 2h/R}{1 - h/R} = \left( 1 - \frac{2h}{R} \right)\left( 1 - \frac{h}{R} \right)^{- 1} = \left( 1 - \frac{h}{R} \right)$
$\therefore\frac{g_{1}}{g_{2}}$ decreases linearly with $h$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.