Find the altitude at which the acceleration due to gravity is 25% of that at the surface of the Earth.
Find the altitude at which the acceleration due to gravity is 25% of that at the surface of the Earth.
(Radius of the Earth = 6400 km)
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Given: gh = 25% of g = \(\frac{25}{100}\times\,g=\frac{g}{4}\),
R = 6400 km = 6.4 × 106 m
To find: Height (h)
Formula: gh = \(g(\frac{R}{R+h})^2\)
Calculation: From formula,
\(\frac{g}{4}=g(\frac{R}{R+h})^2\)
(R + h)2 = 4R2
R + h = 2R
∴ h = 2R – R
∴ h = R
∴ h = 6400 km
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