Expression for acceleration due to Gravity
OR Relation between G and g
Consider a body of mass ‘m’ is lying on earth’s surface as shown in the figure.
According to Newton’s law of gravitation force acting between earth and the body is
F = G Mm /R2 ……………………(1)
From Newton’s 2nd law of motion
F = mg …………………………(2)
from equation (1) and (2)
mg = GMm /R2
g = GM / R2
From above it is clear that ‘g’ is independent on mass of body, shape and size of the body falling under gravity.