First slide

Gravitational field intensity

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

$W = m g - - - (1) g' = \frac{G M}{{(R + h)}^{2}} = \frac{G M}{{(R + \frac{R}{2})}^{2}} = \frac{g R^{2}}{{(\frac{3 R}{2})}^{2}} = \frac{g R^{2}}{\frac{9 R^{2}}{4}} = \frac{4}{9} g ∴ W' = m g' = \frac{4 m g}{9} = \frac{4 W}{9}$

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