Gravitation - Result Question 14
14. A body weighs $72 N$ on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?
[2020]
(a) $32 N$
(b) $30 N$
(c) $24 N$
(d) $48 N$
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Answer:
Correct Answer: 14. (a)
Solution:
- (a) Weight of a body on the surface of the earth, $W_S=m g s=72 N$
Acceleration due to gravity, $g$ varies with height,
$ \begin{aligned} & h=\frac{R}{2} \text{ (given) } \\ W_h & =\frac{m g s}{(1+\frac{h}{R})^{2}}=\frac{72}{(1+\frac{R / 2}{R})^{2}}=\frac{72}{(3 / 2)^{2}} \\ = & \frac{4}{9} \times 72=32 N \end{aligned} $
