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 - (d)/(R_e))`

At earth surface, mg = 600 N ...1)

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

Dividing 1) and 2), we get :

`(g)/(g') = (600)/(300)\\\\(g)/(g') = 2\\\\g = 2g'\\\\g = 2* g* ( 1 - (d)/(R_e) )\\\\1 - (d)/(R_e) = (1)/(2) \\\\d = (R_e)/(2)`

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