First slide

Gravitational field intensity

Question

An object weights 72 N on earth. Its weight at a height of R/2 from earth is

Easy

A

32 N
B

56 N
C

72 N
D

Zero

Solution

$W = m g = 72 N - - - (1) g^{'} = \frac{G M}{{(R + h)}^{2}} = G M {(\frac{1}{R + h})}^{2} = G M {(\frac{1}{R + \frac{R}{2}})}^{2} = G M {(\frac{1}{\frac{3 R}{2}})}^{2} = \frac{G M}{R^{2}} {(\frac{2}{3})}^{2} = \frac{4}{9} g (∵ g = \frac{G M}{R^{2}}) ∴ W' = \frac{4}{9} \times W = \frac{4}{9} \times 72 = 32 N$

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