Question

find out the expression of acceleration due to gravity, when a mass object enter in the earth at depth 'd' and also draw the graph between change in acceleration due to gravity and depth. if mass of the earth is Me​

Answer 1

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Answer 2

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Expression for acceleration due to gravity

~ To derive an expression for acceleration due to gravity, lets take the example of an object placed on the earth.

Let 'M' be the mass of the earth.

Let 'R' be the radius of the earth.

~ If we drop a body of mass 'm', the force excerted by the earth on the body is given by Newton's Law of Gravitation or Universal Law of gravitation.

The Force produces an acceleraion 'g' on the body of mass 'm'.

According to Newtons 2nd law of motion,

F = mg → 1

To Magnitude of the gravitational force between the earth and an object on the surface of the earth we use,

$F = G Mm / r^2$... .. ... ... ... .. (1)

M = Mass of Earth

m = Mass of object

we know F = mg put this in eq(1)

$mg = G Mm / R^2$

g = GM / R^2

This Is the relation!

~ here 'G' does not depend on the mass of the body. It changes slightly from place to place. But for most purposes, it is taken as 9.8 m/s.