## 1. Summary

Every object in the universe attracts the other with a force. This is by virtue of the mass of the objects. This force of attraction was supposed to be thought upon by Newton while contemplating on the free fall of an apple towards the ground. The force of attraction, which is the gravitational pull due to mass of objects, exists universally. The factors that affect gravitational force were studied and a law was put forth which is known as 'Newton's Universal Law of Gravitation'.

The gravitational force between two objects in the universe is directly proportional to the mass of the objects and is inversely proportional to the square of the distance between them. Hence, the mathematical form of the law is where 'm_{1}', 'm_{2}' are the masses of the objects and 'r' is the distance between them. Equating both sides of the expression we get, where, G is the constant of proportionality called the 'universal gravitational constant'.

What do we mean by the mass of a body? It is not easy to define certain fundamental quantities like “mass”. One way of defining it is on the basis of the fact that the mass of an object is the measure of its inertia. Such a mass is known as “inertial mass”. If a force “F” acting on a body produces an acceleration “a” in the body, then, its inertial mass is defined as the ratio of “F” and “a”.

The SI unit for mass is the “kilogram”. When a body is placed in the earth’s gravitational field, the body is attracted by the earth. The force with which the earth attracts a body is known as the “weight of the body”.

If the acceleration gained by a body due to the earth’s gravitational attraction is “g,” then its weight is equal to “mg”.

Weight of a body = mg

Since the “weight” of an object is a force, its SI unit is the “newton”.

The weight of a body is a vector quantity, and always acts towards the centre of the earth. If a body is taken from the “earth” to the “moon”, then there will be no change in its mass, but its weight will decrease. This is because the moon attracts the body with less force than that exerted by the earth. In fact, the weight of a body on the surface of the moon is only one-sixth of its weight on the surface of the earth.

**Gravity**:

The force of attraction exerted by earth on any other body

**Gravitational force**:

The force with which all bodies in the universe attract each other

**Centripetal force**:

A force exerted on a body moving in a circular path, acting towards the centre of the circular path

**Free fall:**

A body falling only under the influence of the force of gravity

**Acceleration due to gravity**

The acceleration of a free falling body due to gravitational force of the earth

**Mass:**

The amount of matter contained in a body

**Weight: **

The force with which a body is pulled towards the centre of the earth