Question

Plot a graph showing the variation of acceleration due to gravity with the center of the earth.
The weight of a body on the surface of earth is $250N$. Calculate its weight at distance equal to half of the radius of earth below the surface of earth. (Radius of earth $=6400km$).

Answer 1

We know that-

$g=\frac{GMx}{R^3}$ for $x<R=$ radius of earth

And $g=\frac{GM}{x^2}$ for $x\ge R$

At surface, $g=\frac{GM}{R^2}=9.8m/s^2$

At half the radius of earth, $x=\frac{R}{2}$

$g^{\prime }=\frac{GMx}{R^3}=\frac{GM\frac{R}{2}}{R^3}=\frac{1}{2}\frac{GM}{R^2}$

$⟹g^{\prime }=4.9m/s^2$

and hence weight will also get halved.

$\therefore weight=125N$