Question

The weight of a body on the surface of the earth is $63N$ . What is the gravitational force on it due to the earth at a height equal to half the radius of earth?

• A. 28 N
• B. 23 N
• C. 12 N
• D. 67 N

Answer 1

Answer: (A)

Given h $=\frac{R_e}{2}$
Acceleration due to gravity at altitude $h$ is given by
$(g{)}^{\prime }=\frac{g}{{\left(1+\frac{h}{(R{)}_e}\right)}^2}$
$=\frac{g}{{\left(1+\frac{(R{)}_e/2}{(R{)}_e}\right)}^2}$
$=\frac{g}{{\left(1+\frac{1}{2}\right)}^2}$
$=\frac{g}{(3/2{)}^2}=g^{\prime }=\frac{4}{9}g\dots$ (i)
Weight of the body at earth's surface
$w=mg=63N\dots$..(ii)
Weight of the body at altitude $h=R_e/2$
$w^{\prime }=m{g}^{\prime }=\frac{4}{9}mg\dots$ (iii)
Using Eq. (ii), we get
$w^{\prime }=\frac{4}{9}\times 63$
$w^{\prime }=28N$