Question

Derive the relation between G and g​

Answer 1

Answer:

Consider earth as an object of mass M and radius R and an object of mass m that is at a distance of r from the centre of the earth.

According to Newton's law of gravitation, we know that the force of attraction exerted by the Earth on the body is as follows:

F = $G\dfrac{Mm}{d^2}$ → Equation 1

When an object falls to the centre of the earth due to gravitational pull, the acceleration is caused by acceleration due to gravity (g).

As per Newton's second law of motion, F = mg → Equation 2

Taking Equation 1 and Equation 2,

mg =  $G\dfrac{Mm}{d^2}$

g = $G\frac{M}{d^2}$

This is the relation between g and G.

Knowledge Bytes

→ G refers to the universal gravitational constant, that is, the force of attraction between any two particles in the universe is represented by the letter G.

→ g refers to the acceleration acting on a body under free fall that is also known as acceleration due to gravity.