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What will be the height above surface of the earth where the value of gravitational acceleration is one forth of that at surface ?

What will be the height above surface of the earth where the value of gravitational acceleration is one forth of that at surface ?

Grade:11

1 Answers

Vikas TU
14149 Points
5 years ago
Gravity acceleration above the earth is given by the formulae: => geff. = GM/(h + R)^2
where h is the distance from the earth’s surface.
g at surface => GM/R^2
Now when it is 1/4th of when it is at surface that is geff. = g/4
Putting both the values we get,
GM/4R^2 = GM/(h + R)^2
(h + R)^2 = 4R^2
h + R = 2R
h = R
Hence at R distance it will be 1-fourth to the value at surface.

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