Question

A body weighs $72N$ on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

• A. 28 N
• B. 32 N
• C. 72 N
• D. 16 N.

Answer 1

Answer: (B)

Weight of body on the surface of the earth $=mg=72N$
Acceleration due to gravity at height h is

$g_h=\frac{g{R}_E^2}{{(R_E+h)}^2}$

Substitute $h=\frac{R_E}{2}$ in above expression:

$g_h=\frac{g{R}_E^2}{{(R_E+\frac{R_E}{2})}^2}$

$=\frac{4}{9}g$

Gravitational force on body at height h is

$F=m{g}_h$

$=m\times \frac{4}{9}g=\frac{4}{9}\times mg$

$=\frac{4}{9}\times 72N=32N$