Question

A body weighs $100N$ at a distance $\frac{R}{4}$ from centre of earth. Find its weight at height of $9R$ from the surface of earth (R - Radius of earth)

• A. $400N$
• B. $3.6N$
• C. $1N$
• D. $4N$

Answer 1

The correct option is D $4N$

distance $=\frac{R}{4}$

$\therefore$ Depth $=d=\frac{3R}{4}$

$g_a=g(1-\frac{d}{R})$

$=g(1-\frac{3}{4})$

$=\frac{g}{4}$

$\therefore 100N=\frac{mg}{4}$

or $mg=400N$

Also, $g_n=\frac{g}{{(1+\frac{h}{R})}^2}$

Distance $=9R$

$\therefore$ Height, $h=8R$

$g_h=\frac{g}{{(1+\frac{8R}{R})}^2}\Rightarrow g_h=\frac{g}{9^2}$

$g_h=\frac{g}{81}$

or $mg=81m{g}_h$

$\Rightarrow 400=81g_{h}m$

or $m{g}_h=\frac{400}{81}\approx 4N$