#### Question

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 weighed 250 N on the surface?

#### Solution 1

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 = `1/2R_e`

Where

`R_e` = Radius of Earth

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

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

`=(1-(R_e)/(2xxR_e))g = 1/2 g`

Weight of the body at depth *d*,

W' = mg

`= mxx1/2g = 1/2 mg = 1/2 W`

`=1/2 xx 250 = 125 N`

#### Solution 2

As`g_d = g(1-d/R) => mg_d = mg(1-d/R)`

Here `d= R/2`

`:. mg_d = (250)xx (1-"R/2"/R) = 250 xx 1/2 = 125 N`

Is there an error in this question or solution?

Solution 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 Weighed 250 N on the Surface Concept: Acceleration Due to Gravity of the Earth.