# A body, whose momentum is constant, must have constant:

(A) Force

(B) Velocity

(C) Acceleration

(D) All of these

Answer

Verified

174.6k+ views

**Hint: -**Momentum is simply defined as the mass in motion. All the objects have mass, consequently, if the object is moving it possesses momentum. The momentum of a body is the product of its mass and the velocity by which the object is moving. The point to be kept in mind while solving this question is that the momentum is directly proportional to its velocity, keeping its mass to be constant.

**Complete step-by-step solution:**

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.

**As a result, the right option is (D) All of these.**

**Note:**

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.

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Name the Largest and the Smallest Cell in the Human Body ?

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

A ball impinges directly on a similar ball at rest class 11 physics CBSE

Lysosomes are known as suicidal bags of cell why class 11 biology CBSE

How do you define least count for Vernier Calipers class 12 physics CBSE

Two balls are dropped from different heights at different class 11 physics CBSE

A 30 solution of H2O2 is marketed as 100 volume hydrogen class 11 chemistry JEE_Main