Question

The value of $g$ at a height equal to half the radius of the earth from the earth's surface is

• A. $\frac{g}{2}$
• B. $\frac{g}{3}$
• C. $\frac{4g}{9}$
• D. $\frac{g}{4}$

Answer 1

Answer: (C)

Acceleration due to gravity at a height $h$
from the earth's surface is $g_{h} = \frac{gR^{2}_{E} }{\left(R_{E} +h\right)^{2}}$
where g is acceleration due to gravity on the earth's surface.
At $ h =\frac{R_{E}}{2} ,g_{h} = \frac{gR^{2}_{E}}{\left( R_{E} +\frac{R_{E}}{2}\right)^{2}} = \frac{4}{9}g$