Question

variation of g with shape​

Answer 1

Explanation:

The shape of the earth is bulged at the equator and flat at the poles. This means earth has large radius at the equator than at poles.

We know that,

So, acceleration due to gravity is more at the pole than at the equator.

Answer 2

Variation of Acceleration due to to gravity (g) due to shape of Earth:-

Let:-

• The Radius of Earth passing through poles be = Rp

• The Radius of Earth passing through equator be = Re

• G= Gravitational Constant

• M = Mass of Earth

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Need to know;-

• We know the shape of Earth is not actually round.

• And The Radius of Earth via Equator > Radius of Earth via pole.

• Re = Rp + 21000 m

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We know:-

$g = \dfrac{GM}{ {R}^{2} }$

so,

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→The Acceleration due to gravity at poles :-

${g}_{p} = \dfrac{GM}{( {{R}_{p}}^{2} )}$

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→The Acceleration due to gravity at equator :-

$g = \dfrac{GM}{ {Re}^{2} }$

→ $g = \dfrac{GM}{ {(Rp + 21000)}^{2} }$

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Clearly

$\dfrac{GM}{ {(Rp + 21000)}^{2} }$ < $\dfrac{GM}{( {{R}_{p}}^{2} )}$

Or,

$\red{\boxed {\bold {\large{\implies{g}_{e} < {g}_{p}}}}}$

Thus the value of Acceleration due to gravity (g) decrease as we move towards equator from the poles.