Question

What is the weight of a body at a depth equal to half the radius of earth, if it weighs $250\text{N}$ on the surface of earth?

• A. $200\text{N}$
• B. $125\text{N}$
• C. $105\text{N}$
• D. $75\text{N}$

Answer 1

The correct option is B $125\text{N}$


Given:
$W=250\text{N};d=R/2$

The acceleration due to gravity at a depth $d$ from the surface is given by

$g^{\prime }=g(1-\frac{d}{R})$

$\Rightarrow g^{\prime }=g(1-\frac{R/2}{R})=\frac{g}{2}$

Given that the weight of body at the surface of earth is given by

$W=mg=250\text{N}$

So, at depth $d=R/2$, weight $W^{\prime }$ will be

$W^{\prime }=m{g}^{\prime }=\frac{mg}{2}=\frac{250}{2}=125\text{N}$

Hence, option $\left(b\right)$ is correct.