First slide

Variation of g

Question

A body weighs 180 N on the surface of earth (Radius=R). How much does the body weigh at a height $\frac{R}{2}$ above the surface of earth?

Easy

A

80 N
B

120 N
C

160 N
D

140 N

Solution

On the surface of earth $W = m g = m . \frac{G M}{R^{2}}$
At a height $\frac{R}{2}$ above the surface of earth
$W^{1} = m g^{1} = m \frac{G M}{{(R + \frac{R}{2})}^{2}} = \frac{4}{9} \frac{G M m}{R^{2}} = \frac{4 W}{9}$
$\Rightarrow W^{1} = \frac{4}{9} \times 180 N = 80 N$

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