Variation of Gravity with Height – Rankers Physics
Topic: Gravitation
Subtopic: Acceleration Due to Gravity and its variation

Variation of Gravity with Height

The height at which the weight of a body becomes 1/9th its weight on the surface of earth (radius of earth is R):
\(h = 3R\)
\(h = R\)
\(h = \frac{R}{2}\)
\(h = 2R\)

Solution:

Since acceleration due to gravity varies with height as \(g' = g \frac{R^2}{(R+h)^2}\), setting \(g' = g/9\) gives \(R+h = 3R\), which simplifies to \(h = 2R\).

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