Ncert Exercises & Solutions

8.16 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?

Given,

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

= \frac{1}{2} R_{e}

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

g = (1 - \frac{d}{R_{e}}) g

= (1 - \frac{R_{e}}{2 \times R_{e}}) g

= \frac{1}{2_{}} g

Weight of the body at depth d,

W' = mg

= m \times \frac{1}{2} g = \frac{1}{2} mg = \frac{1}{2} W

= \frac{1}{2} \times 250 = 125 N

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