Question

Weight of a body on earth's surface is $W$. At a depth half way to the centre of the earth, it will be (assuming uniform density in earth).

• A. $W$
• B. $W/2$
• C. $W/4$
• D. $W/8$

Answer 1

The correct option is B $W/2$

The variation of g with depth is given by

$g^{{}^{\prime }}=\frac{g}{1-\frac{d}{R}}$ where d is depth

At a depth half way to the centre of the earth $d=\frac{R}{2}$

$g^{{}^{\prime }}=\frac{g}{1-\frac{R}{2R}}$

$g^{\prime }=\frac{g}{2}$

On multiplying both sides by m

$m{g}^{\prime }=\frac{mg}{2}$

$W^{{}^{\prime }}=\frac{W}{2}$

At the depth half way, weight becomes half.