Question

how to derive the value of 'g' in gravitation

Answer 1

According to the Universal Law of Gravitation,
Force between 2 objects=
GM1M2/R^2
but on Earth weight of an object = M2g
and the force between the earth and an object = its weight
thus, GM1M2/R^2=M2g
and so, g=GM1/R^2
Now, by putting in the values of G, M1 and R
the value of g comes out to be approximately 9.81m/s^2.
It is to be noted that M1=Mass of Earth M2=Mass of object G=Universal gravitational constant R=Radius of Earth.

Answer 2

well the value of g in gravitatoin cant be derived ...
it is constant and has fixed value..ie.
g= 9.8 m/s..

but the value of gravitational force between
earth and body can be derived...i.e
F=m.a..
but
a=1/r^2
therefore..
F=m/r^2
According to newtons third law ..
force on the body due to earth is equal to force on earth due to body..
hence,
F is directly proportional to (M.m/r^2).
so,
F=GMm/r^2

where G is univesal gravitation constant and has value 6.67 ×10^-11 Nm^2/kg^2..

This is how it is proved....