Question

RELATION BETWEEN ACCELERATION DUE TO GRAVITY AND UNIVERSAL CONSTANT OF GRAVITATION

Answer 1

We know that
F(gravitational force) = GmM/r²
Where G is universal gravitational constant. And m and M are masses of objects kept at a distance of r from their centers .
And F(gravity) = m×g { g=acceleration due to gravity

This gives
mg = GmM/r²
=> g = GM/r²

Answer 2

hey there !!!

◆ we know from classical mechanics /// '' according to the Newton's law of gravitation :--

**forces between two particle is directly proportional to its product of masses and inversely proportional to the square of distance between them..**

so, mathematically ,

=). F ¢ m1×m2 --------(1)

=) F ¢ 1/r^2 ----------(2)

combining both we get ,

F = G m1×m2/ r^2 -----------(3)

And , we also know that "g" is acceleration due to gravity ..

=) F = mass ×acceleration

=) F = m×g

so in case of earth and particle ...

Let us consider mass of earth is M and that of partical is m

so =) F = G Mm/r^2 ----------(a)

=) F = mg -------------(b)

so both equations are equal,

=). mg = G Mm/ r^2

cancel out 'm' from both sides . we get,

=) ( g = GM/r^2 )

Now ,
◆ here we can see that 'g' depends on universal gravitational constant (G) AND mass of earth (M) AND distance of partical from the centre of earth (r).

◆ so we can say that 'g' is a variable quantity that changes from place to place ...
But G remains constant throughout the universe..

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HOPE IT WILL HELP U