First slide

Acceleration due to gravity and its variation

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)

Moderate

A

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

$0, \frac{3 R}{4}$
C

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

$\frac{3 R}{4}, 0$

Solution

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

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