Question

mathematically show that the magnitude of 'g' remains same at a particular place

Answer 1

Answer:

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Answer 2

To show:

The magnitude of gravitational acceleration remains same at a particular place.

Proof:

Gravitational acceleration is a representation of gravitational field intensity at any place with respect to the centre of the planet.

Let radius of earth be r ;

Let us assume that an object of mass M has been kept on the surface of the earth;

Following Newton's Law;

$\therefore \: \sf{force = \dfrac{G(M \times m)}{ {r}^{2} } }$

$= > \: \sf{m \times g = \dfrac{G(M \times m)}{ {r}^{2} } }$

$= > \: \sf{ g = \dfrac{GM }{ {r}^{2} } }$

So, "g" remains constant if the "r" value remains same.

Hence , magnitude of g will remain constant at any particular place.

[Hence Proved].