If the force inside the earth surface varies as $x^{n}$, where $r$ is the distance of body from the centre of earth, then the value of $n$ will be

Question

Dr. Abubacker · Accepted Answer

(c) Force acting on a body of mass $M$ at a point at depth $d$. Inside the earth is
$F = mg^{'} = mg\left( 1 - \frac{d}{R} \right)$
$= \frac{mGM}{R^{2}}\left( \frac{R - d}{R} \right) = \frac{GM\ m}{R^{3}}r\ \ (\because R - d = r)$
So, $F \propto r;$ Given $F \propto r^{n}$
$n = 1$

Q. If the force inside the earth surface varies as $x^{n}$, where $r$ is the distance of body from the centre of earth, then the value of $n$ will be

Explanation

Reviewed by Dr. Abubacker

Want more practice?