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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

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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

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`

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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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