# Inertial and Gravitational Mass

## law

### Inertial and Gravitational mass

1) Inertial mass

This is defined by Newton's 2nd law-  F = ma, which states that when a force F is applied to an object, it will accelerate proportionally, and that constant of proportion is the mass of that object. In very concrete terms, to determine the inertial mass, you apply a force of F Newtons to an object, measure the acceleration in m/s2, and F/a will give you the inertial mass m in kilograms.

2) Gravitational mass

This is defined by the force of gravitation, which states that there is a gravitational force between any pair of objects, which is given by

where G is the universal gravitational constant, and are the masses of the two objects, and r is the distance between them. This, in effect defines the gravitational mass of an object.

Gravitational mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass. This is typically done by balance scale.

## definition

### equivalence principle in einstein's general relativity

Consider following three conditions to understanding the Equivalence of Inertial and Gravitational mass.

1. let's consider a person standing in spaceship resting on earth. His feet on the floor of the ship. Now we know the normal force is equal to an apparent weight of person which is mg, As acceleration a = 0 (spaceship at rest). Hence normal force = apparent weight = mg.

2. Man in a spaceship which is very far from the planet and he is floating in the ship, hence acceleration a = 0. An apparent weight of man becomes zero (weightlessness).

3. Man in a spaceship which is accelerating with acceleration a = g in space, now the apparent weight of man becomes mg. A spaceship is far away from planet there is no any g due to the planet. But man touching the floor and it gives the normal force to man which give the apparent weight = mg.

Hence the force due to gravity is same as that of acceleration. Hence there is an equivalence between inertial and gravitational mass.