Fractional change in gravity with depth – Rankers Physics
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Fractional change in gravity with depth

The fractional change in acceleration due to gravity on surface of earth (g) when the body is taken to a depth h from the surface of earth, is (where R = radius of Earth)
\(1 - frac{h}{R}\)
\(frac{h}{R}\)
\(1 - frac{2h}{R}\)
\(frac{2h}{R}\)

Solution:

The acceleration due to gravity at depth \(h\) is \(g_d = gleft(1 - frac{h}{R}right)\. The change in gravity is \(Delta g = g - g_d = gfrac{h}{R}\). Thus, the fractional change \(frac{Delta g}{g}\) is \(frac{h}{R}\).

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