Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighd 250 N on the surface ?

Explanation

Weight of a body of mass m at the Earth's surface, `W=mg=250 N`

Body of mass m is located at depth, `d`=`(R_e/2)`

Acceleration due to gravity at depth `g(d)` is given by the relation:

`g^'`=`(1-d/R_e)``g`

`g^'`=`g/2`

Weight of the body at depth `d`,


`W^'`=`mg^'`=`(mg/2)`=`(W/2)`=`125N`