Question

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

• A. $16N$
• B. $32N$
• C. $8N$
• D. $48N$

Answer 1

The correct option is B $32N$

Given that,

Weight $W=72N$

Height $=h$

Now, the acceleration due to gravity at a height h from the surface of the earth

$g_h=g{\left(\frac{R}{R+h}\right)}^2$

$g_h=g{\left(\frac{R}{R+\frac{R}{2}}\right)}^2$

$g_h=g{\left(\frac{2R}{3R}\right)}^2$

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

Now, the gravitational force on the body at a height h is

$F=m{g}_h$

$F=72\times \frac{4}{9}$

$F=32N$

Hence, the gravitational force is $32N$