Question

A body, whose momentum is constant, must have constant
A. Force
B. Velocity
C. Acceleration
D. All of these

Answer 1

Hint: As the fourth option is ‘all of these’, there is a possibility of all the three being constant. Firstly, let us recall the definition and hence the expression for the momentum. Then you could recall the expression for Newton’s second law of motion. Using these two expressions you will be able to easily determine the answer.

Complete Step by step solution:
In question, we are given a body whose momentum is said to be constant. Then, we are asked to find which among the given quantities in the options must be constant so as to satisfy the given condition.
You may recall that the momentum of a body is given by the product of mass and velocity. That is, momentum p can be given by,
$p=mv$
Where, m is the mass of the body and v is its velocity.
Now, it is quite obvious that mass and velocity should definitely be constant for the momentum of a body to be constant.
Now, let us recall Newton’s second law of motion, which expresses the time rate of change of momentum as the force. That is, by Newton’s second law,
$\dfrac{dp}{dt}=F=ma$
But when, momentum p is constant,
$\dfrac{dp}{dt}=0$
$\Rightarrow F=ma=0$
Therefore, we found that for constant momentum, the force as well as the acceleration of the body will definitely be zero.
So, we found that for a body, whose momentum is constant, the velocity must be constant.

Hence, option B is found to be the correct answer.

Note:
The SI unit of momentum is $kg.m/s$. Momentum is known to be a vector quantity that has both magnitude as well as direction. The direction of the momentum vector will be the same as the velocity of the body as the mass of the body is a scalar quantity. Both the variables, that is, mass and velocity, have equal importance in determining the value of momentum.