Question

The distances from the centre of the earth where the weights of the body is zero and one fourth that of the weight of body on the surface of earth respectively are___ (Assume $R$ is the radius of the earth)

• A. $0,\frac{R}{4}$
• B. $0,\frac{3R}{4}$
• C. $\frac{R}{4},0$
• D. $\frac{3R}{4},0$

Answer 1

The correct option is A $0,\frac{R}{4}$

Variation of gravity with depth$\left(d\right)$ is given by
$g_1=g(1-\frac{d}{R})$
Case $\left(i\right)$
If weight of the body is zero $g_1=0$
$g_1=g(1-\frac{d}{R})=0\Rightarrow d=R$
Depth from surface =$R$
Distance from centre=$0$

Case $\left(ii\right)$ $g_1=\frac{g}{4}$
$\frac{g_1}{g}=(1-\frac{d}{R})=\frac{(R-d)}{R}\Rightarrow R-d=\frac{g/4}{g}R=\frac{R}{4}$
$\Rightarrow d=\frac{3R}{4}$
Depth from surface =$\frac{3R}{4}$
Distance from centre=$R-\frac{3R}{4}=\frac{R}{4}$.