Question

A body weight $ 45\,N $ on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half of the radius of the earth?

• A. $ 20\,\,N $
• B. $ 45\,\,N $
• C. $ 40\,N $
• D. $ 90\,N $

Answer 1

Answer: (A)

Acceleration due to gravity at $h=\frac{R}{2}$
$g'=\frac{g}{\left(1+\frac{h}{R_{e}}\right)^{2}}=\frac{g}{\left(1+\frac{R_{e}}{2 R_{e}}\right)^{2}}$
$=\frac{g}{\left(\frac{3}{2}\right)^{2}}=\frac{4}{9} g$
$\Rightarrow $ So $w'=\frac{4}{9} $
$w=\frac{4}{9} \times 45=20\, N$