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  • A body weighs 72 N on the surface of the earth. WHat is the gravitational force on it, at a height equal to half of the radius of the earth?Option: 1 <p

A body weighs 72 N on the surface of the earth. WHat is the gravitational force on it, at a height equal to half of the radius of the earth?

Option: 1

48 N


Option: 2

32 N


Option: 3

30 N


Option: 4

24 N


Answers (1)

\\ \text{Weight of body on the surface of the earth} =\mathrm{mg}=72 \mathrm{N}\\ \text {Acceleration due to gravity at height h is}\\ g_{h}=\frac{g R_{E}^{2}}{\left(R_{E}+h\right)^{2}} =\frac{\mathrm{gR}_{\mathrm{E}}^{2}}\ \ \ {\left(\mathrm{R}_{\mathrm{E}}+\frac{\mathrm{R}_{\mathrm{E}}}{2}\right)^{2}} =\frac{4}{9} g\left(\because h=\frac{R_{E}}{2}\right) \\ \text {Weight of body at height }\mathrm{h} is \mathrm{}=\mathrm{mg}_{\mathrm{h}} =\mathrm{m} \times \frac{4}{9} \mathrm{g}=\frac{4}{9} \times \mathrm{mg} =\frac{4}{9} \times 72 \mathrm{N}=32 \mathrm{N}

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Kshitij

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