Gravitation - Result Question 22
22. A body weighs $72 N$ on the surface of the earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?
[2000]
(a) $32 N$
(b) $28 N$
(c) $16 N$
(d) $72 N$
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Answer:
Correct Answer: 22. (a)
Solution:
- (a) $m g=72 N$ (body weight on the surface)
$ g=\frac{G M}{R^{2}} $
At a height $H=\frac{R}{2}$,
$ \begin{aligned} g^{\prime} & =\frac{G M}{(R+\frac{R}{2})^{2}} \\ & =\frac{4 G M}{9 R^{2}} \end{aligned} $
Body weight at height $H=\frac{R}{2}$,
$ \begin{aligned} & m g^{\prime}=m \times \frac{4}{9}(\frac{G M}{R^{2}}) \\ & =m \times \frac{4}{9} \times g=\frac{4}{9} m g \\ & =\frac{4}{9} \times 72=32 N \end{aligned} $
