Question

The distances from the centre of the earth, where the weight of a body is zero and one-fourth that of the weight of the body on the surface of the earth 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

Answer: (A)

$0$, $\frac{R}{4}$

The weight of the body at the centre of the earth is equal to zero because
$g_{centre}=g(1-\frac{d}{R})=g(1-\frac{R}{R})=0$
$\frac{g_1}{g}=(1-\frac{d}{R})=\frac{1}{4}\Rightarrow d=\frac{3R}{4}$
So from the centre, $d=\frac{R}{4}$