Question

if your weight is 600 Newton on the earth how far should you go from the centre of the earth so that it will be 300 Newton​

Answer 1

Given :

Our weight is 600 Newton on the earth.

To Find :

How far should you go from the center of the earth so that it will be 300 Newton​.

Solution :

Acceleration due to gravity at depth d is given by :

$g' = g( 1 - \dfrac{d}{R_e})$

At earth surface, mg = 600 N   ...1)

At depth d, mg' = 300 N            ...2)

Dividing 1) and 2), we get :

$\dfrac{g}{g'} = \dfrac{600}{300}\\\\\dfrac{g}{g'} = 2\\\\g = 2g'\\\\g = 2\times g\times ( 1 - \dfrac{d}{R_e} )\\\\1 - \dfrac{d}{R_e} = \dfrac{1}{2} \\\\d = \dfrac{R_e}{2}$

Therefore, we should go in the depth of distance half the radius of earth.