First slide

Acceleration due to gravity and its variation

Question

A man weigh ‘W’ on the surface of the earth and his weight at a height of ‘R’ from surface of earth is (Radius of the earth)

Easy

A

$\frac{W}{4}$
B

$\frac{W}{2}$
C

$W$
D

$4 W$

Solution

$g = \frac{G M}{R^{2}} & g_{h} = \frac{G M}{{(R + h)}^{2}} \Rightarrow \frac{g_{h}}{g} = {(\frac{R}{R + h})}^{2} W = m g; W^{'} = m g^{'} = m g {(\frac{R}{R + h})}^{2} = W {(\frac{R}{R + R})}^{2} = W {(\frac{R}{2 R})}^{2} = \frac{W}{4}$

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