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Question

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(A) Force

(B) Velocity

(C) Acceleration

(D) All of these

Answer

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In Newtonian mechanics, momentum is the product of the mass and velocity of a body. If $m$ is the mass of an object and $v$ be its velocity, then the body’s momentum $p$ is:

$p = mv$ ........... $\left( 1 \right)$

Since the momentum is directly proportional to its velocity. If the momentum of a body is constant then its velocity also becomes constant.

As we know that the rate of change in velocity is the acceleration,

$a = \dfrac{{dv}}{{dt}}$ ............. $\left( 2 \right)$

Since the velocity becomes constant,

$\therefore dv = 0$

Substitute the value in the equation $\left( 2 \right)$ ;

$ \Rightarrow a = \dfrac{0}{{dt}}$

$ \Rightarrow a = 0$

So, the acceleration of the body having momentum constant is zero.

Thus we can say that when the momentum of a body is kept constant then its acceleration becomes zero or constant.

Furthermore, Newton’s second law of motion states that the rate of change of momentum of a body is equal to the net force acting on it. If $\Delta p$ be the change in momentum and $\Delta t$ be the time interval, then the net force acting on the body can be given:-

$F = \dfrac{{\Delta p}}{{\Delta t}}$ ............... $\left( 3 \right)$

We have given that the momentum of a body is constant

$\therefore \Delta p = 0$

Substitute the value in the equation $\left( 3 \right)$

$F = \dfrac{0}{{\Delta t}}$

$ \Rightarrow F = 0$

Thus the net force applied on a body having a momentum constant is zero.

It is important to note that for a closed system, the total momentum is constant. This is well-known as the ‘law of conservation of momentum’. This law applies to all interactions, including collisions, no matter how complicated the force is between the particles.