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8.15 A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

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Vishal Baghel | Contributor-Level 10

5 months ago

Weight of the body, W = 63 N

Acceleration due to gravity at h from the Earth's surface is given by

g' = $\frac{g}{{(\frac{1 + h}{R_{e}})}^{2}}$ where g = acceleration due to gravity on the Earth's surface, $R_{e}$ = Radius of the Earth. h = $\frac{R_{e}}{2}$

g' = $\frac{g}{{(\frac{1 + R_{e} / 2}{R_{e}})}^{2}}$ = $\frac{g}{{(\frac{1 + h}{2 h})}^{2}}$ = (4/9)g

Weight of the body of mass m at a height h is given by

W' = m X g' = (4/9) mg = (4/9) x w = (4/9) x 63 N = 28 N

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8.15 A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

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