# State and prove Newton’s 3rd Law

Newton’s third law is a very important law and very common law. Consider two objects 1 and 2 moving along the same straight line in an isolated system. Let the two bodies mutually collide so that they act or react with each other. Due to collision, the velocity of the two bodies change, and hence their momenta also change.

Let delta p_{1 }+delta p_{2} = 0

Or delta p_{2} = -delta p_{1}

Dividing both sides by delta t and taking limits delta t → 0

dp2/dt = dp1/dt

The above equation shows that the rate of change of momentum of body 2 is equal to the negative rate of change of momentum of body 1.

i.e. Force on 2 = – force on 1

that is action and reaction are equal and opposite.

This is proof of Newton’s third law of motion.

**Significance of Newton’s Third law:**

(i) Newton’s 3^{rd} Law signifies that force in nature occurs in pairs i.e. the single isolated force is not possible.

(ii) The action and reaction forces always act on different bodies. Hence they never cancel each other.

(iii) The force of action and reaction may appear due to the actual physical contact of the two bodies or even from a distance.

(iv) 3^{rd} Law is applicable to the bodies at rest or in motion.

(v) It is applicable to all types of forces.