First slide

Acceleration due to gravity and its variation

Question

What will be the acceleration due to gravity at height h if h >> R. Where R is radius of earth and g is acceleration due to gravity on the surface of earth

Easy

A

$\frac{g}{{(1 + \frac{h}{R})}^{2}}$
B

$g (1 - \frac{2 h}{R})$
C

$\frac{g}{{(1 - \frac{h}{R})}^{2}}$
D

$g (1 - \frac{h}{R})$

Solution

$g^{'} = \frac{G M}{{(R + h)}^{2}} = \frac{g R^{2}}{{(R + h)}^{2}} = \frac{g}{{(1 + \frac{h}{R})}^{2}} (∵ g = \frac{G M}{R^{2}})$

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