First slide

Variation of g

Question

Weight of a body on the surface of earth is 100 N. If R be the radius of earth, then what will be the weight of the body at a height R/2 above the surface of earth?

Easy

A

50
B

25 N
C

44.45 N
D

64.25 N

Solution

$W = m g = \frac{G M m}{R^{2}}$ (on the surface of earth)
At a height h, $W^{1} = m g^{1} = \frac{G M m}{{(R + h)}^{2}}$
$∴ \frac{W^{1}}{W} = {(\frac{R}{R + h})}^{2} = {(\frac{R}{R + \frac{R}{2}})}^{2} = \frac{4}{9}$
$\Rightarrow W^{1} = \frac{4}{9} \times 100 N = 44.45 N$

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