derive expression on acceleration due to gravity - Science - Gravitation

Question

derive expression on acceleration due to gravity

Manan Arora · Accepted Answer

Dear Student, Force acting on a body due to gravity is given by, f
= mg Where f is the force acting on the body, g is the acceleration
due to gravity, m is mass of the body According to the universal
law of gravitation, f = GmM/(r+h)2 Where, f = force between two
bodies, G = universal gravitational constant (6
67Ã—10-11 Nm2/kg2) m = mass of the object, M = mass of
the earth, r = radius of the earth h = height at which the body is
from the surface of the earth As the height (h) is negligibly small
compared to the radius of the earth we re-frame the equation as
follows, f = GmM/r2 Now equating both the expressions, mg = GmM/r2
â‡’ g = GM/r2 Therefore, the formula of
acceleration due to gravity is given by, g = GM/r2 Regards