Ncert Exercises & Solutions

8.15 A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

Given,

Weight of the body, W = 63 N

Acceleration due to gravity at height h from the Earth's surface is given by the relation:

g' = \frac{g}{{(1 + \frac{h}{R})}^{2}}

F o r, h = \frac{R}{2}

g' = \frac{g}{{(1 + \frac{R / 2}{R})}^{2}} = \frac{4}{9} g

T h e r e f o r e, t h e w e i g h t o f t h e b o d y,

W = m g'

= m \times \frac{4}{9} g

= \frac{4}{9} \times 63 g = 28 N

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