First slide

Acceleration due to gravity and its variation

Question

A body weight W newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be

Easy

A

$\frac{W}{2}$
B

$\frac{2 W}{3}$
C

$\frac{4 W}{9}$
D

$\frac{8 W}{27}$

Solution

$g' = g {(\frac{R}{R + h})}^{2} = g {(\frac{R}{R + \frac{R}{2}})}^{2} = g {(\frac{R}{\frac{3 R}{2}})}^{2} = \frac{4}{9} g ∴ W' = m g' = m \frac{4 g}{9} = \frac{4}{9} W$

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