Gravitation Ques 10
10. 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: 10.(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} $
BETA
