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# 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 - CBSE (Science) Class 11 - Physics

ConceptAcceleration Due to Gravity of the Earth

#### 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 (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

Asg_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

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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.
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