Question

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} $

Answer 1

Answer: (A)

The value of acceleration due to gravity $g$ at a 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.
$\therefore \, \frac{g}{g_{h}}=\left(1+\frac{h}{R}\right)^{2}$