Question

Derived the formula for acceleration due to gravity.Below the surface of earth

Answer 1

Acceleration Due To Gravity Above And Below The Earth's Surface. ... The radius of the earth is denoted by Re. Here, the distance of the object from the centre of the earth is (Re + h). Let us say, the magnitude of the force on the point mass m is denoted by F.

Answer 2

ANSWER:-

The distance of the object from the centre of the Earth is given by (Re-d) and the magnitude of the gravitational force acting on the object is F(d).

So,

F(d)=GMsm(Re−d)2

Here, the object can be assumed to be present at the concentric sphere of radius (Re-d).Hence, the mass of the earth contributing to the gravitational force is the mass of the inner concentric sphere.

The equivalent relation between the masses can be given as

MsMe=(Re−d)2R3e

Putting the value of Ms in the equation for gravitational force, we get

F(d)=GMem(Re−d)2R3e

The acceleration due to gravity of point mass m at the given depth of d from the earth surface is given by

g(d)=GMe(Re−d)R3e=GM3R2e×Re−dRe=GMeR2e×1–dRe

As we know that the expression for acceleration due to gravity for an object at the surface of the earth is given by

GMeR2e, we can say that, for an object placed at a height h, the acceleration due to gravity is less as compared to that placed on the surface.

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