Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# There are three Newton’s laws of motion namely first, second and third laws. We can deriveA. Second and third laws from the first lawB. First and second laws from the third lawC. Third and first laws from the second lawD. All the three laws are independent of each other.

Last updated date: 17th Jun 2024
Total views: 52.8k
Views today: 0.52k
Verified
52.8k+ views
Hint Newton's first law states that the object at rest or in other words it is in motion will remain unless the object relates a net external force But the newton's Second Law of Motion relates force, mass, and acceleration.

Complete step by step solution
Newton’s second law of motions states that the net force applied on a body is equal to the rate of change in its Momentum.
We know that, $F = ma$
$a = v - \dfrac{u}{t}$
Substitute, $F = m\left( {v - \dfrac{u}{t}} \right)$
Simplify, $Ft = mv - mu.$
Now, when $F = 0$then $v = u.$ This shows the absence of the force. So, the object continues with the same velocity.
Now, when $F = 0$ and $u = 0$,then $v = 0.$That is, an object at rest if no force is acting on it.
Therefore, first law is derived from the second law.
Now, let us consider a system of two bodies, one and two bodies, there is no force acting on it.
Now ${F_{12}}$ be the force acting on 2 by 1 and ${F_{21}}$ be the force acting on 1 by 2.
The rate of change of the momentum of $1 = \dfrac{{d{p_1}}}{{dt}}$ and the rate of change of the momentum of $2 = \dfrac{{d{p_2}}}{{dt}}$.
$\dfrac{{d\left( {{p_2} + {p_1}} \right)}}{{dt}}$
Therefore, ${F_{12}} + {F_{21}} = 0.$