Question

Give the derivation for acceleration due to gravity (small g)

Answer 1

The acceleration of a freely falling body under the action of gravity of the earth is called acceleration due to gravity
The average value of acceleration due to gravity is denoted by g is taken as 9.8 meter per second square in SI system
Here the derivation is
G is universal gravitons constant of value is equal to 6.673×10 to the power -11 m2/kg2
By Newton second law
F=ma
F is force acting on the object

m is mass and a is acceleration

By Newton law of gravity we can write
Fg = GMm/(r+h) square
It is the gravitational force acting between two bodies lying in gravitational field of each other
Each of the bodies experiences same force directed toward the other

using second law of motion to find acceleration in this condition
a=Fg/m
m means mass of the object for which the acceleration due to gravity is to be calculated
a=g=GMm/(y+h) square

when the object is on or near to the surface the value of g becomes constant an does not change considerably with height.
so , we write g=gM/r square


I hope u under stand
Tq