Q. The ratio$\ \frac{g}{g_{h\ }},$ where$\ g\ $and$\ g_{h}$ are the accelerations due to gravity at the surface of the $\ $earth and at a height $h$ above the earth’s surface respectively, is
A) $\left( 1 + \frac{h}{R} \right)^{2}$
B) $\left( 1 + \frac{R}{h} \right)^{2}$
C) $\left( \frac{R}{h} \right)^{2}$
D) $\left( \frac{h}{R} \right)^{2}$
Explanation
(a) The value of acceleration due to gravity $g$ at height $h$ above the surface of earth is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g_{h} = \frac{g}{\left( 1 + \frac{h}{R} \right)^{2}}$
Where $R$ is radius of earth.
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{g}{g_{h}} = \left( 1 + \frac{h}{R} \right)^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.