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 $g_h=\frac{g{R}_E^2}{{\left(R_E+h\right)}^2}$
where g is acceleration due to gravity on the earth's surface.
At $h=\frac{R_E}{2},g_h=\frac{g{R}_E^2}{{\left(R_E+\frac{R_E}{2}\right)}^2}=\frac{4}{9}g$