Height at which gravity becomes 6.25% – Rankers Physics

Acceleration Due to Gravity and its variation: Practice Problem & Solution

At certain height \(h\) from surface of earth the value of \(g\) become \(6.25%\) of its value at earth surface. The ratio of \(\frac{h}{R}\) is. (\(R\) is radius of earth)
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Solution Explained:

To solve this problem, we apply the core principles of Acceleration Due to Gravity and its variation. Understanding the underlying formula is key to arriving at the correct answer below:

The variation of gravity with height is \(g' = g \left(\frac{R}{R+h}\right)^2\). Given \(g' = 0.0625 g = \frac{1}{16} g\), we get \(\frac{R}{R+h} = \frac{1}{4} ⇒ R+h = 4R ⇒ h = 3R ⇒ \frac{h}{R} = 3\).

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