Topic: Acceleration due to gravity and its variation with altitude and depth· Gravitation

Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by

Starting from the centre of the earth having radius \(R\), the variation of \(g\) (acceleration due to gravity) is shown by

four g vs r graphs (options)

1. graph (1)

2. graph (2)

3. graph (3)

4. graph (4)

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Answer: 1. graph (1)

Inside the earth \(g\) is proportional to the distance from the centre; outside it falls as \(1/r^2\).

For \(r
For \(r>R\): \(g=\dfrac{GM}{r^2}\), a curve that decreases but never becomes zero.

Only graph (1) shows a straight rise up to \(R\) followed by a hyperbola-like fall. Graph (2) is curved inside, graph (3) is constant inside, and graph (4) falls linearly to zero outside.

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Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by

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