Question

A body weighs 100 N at a distance $\frac{R}{4}$ from the center of the earth. Find its weight at height of $9R$ from the surface of the earth ($R$=Radius of earth and answer in SI unit )?

Answer 1

$W_d=100N$ at a distance $\frac{R}{4}$ from centre of earth.
$\therefore d=R-\frac{R}{4}=\frac{3R}{4}$
$\therefore g_d=g(1-\frac{d}{R});g_d=g/4$

Now mass $=\frac{W_d}{g_d}=\frac{400}{g}$

At height 9R
$g_h=\frac{9\left(R^2\right)}{100R^2}=\frac{g}{100}$
$\therefore W_h=m{g}_h=\frac{400}{g}\times \frac{g}{100}=4N$