Question

For constant non zero mass, momentum versus velocity graph is a ?
A. straight line parallel to x-axis
B. straight line parallel to y-axis
C. straight line passing through origin
D. straight line passing through y-axis with an intercept

Answer 1

The point to be kept in mind while solving this question is that the momentum of a body is directly proportional to its velocity, keeping its mass to be constant. And the equation which is a part for this is,
${\text{y = mx}}$ ………..(1)
Which is also called the slope equation of tangent equation which we will use in our solution.

Complete step-by-step answer:
In Newtonian mechanics, momentum is the product of the mass and velocity of a body. If m is mass of an object and be its velocity, then the body’s momentum p is :-
${\text{p = mv}}$ ………..(2)
Moreover, Newton’s second law of motion states that the rate of change of a body’s momentum is equal to the net force acting on it. Momentum depends upon the frame of reference but in any inertial frame, it is a conserved quantity. If $\Delta {\text{p}}$ be the change in momentum and $\Delta {\text{t}}$ be the time interval, then the net force acting on the body can be given by :-
${\text{F = }}\dfrac{{\Delta {\text{p}}}}{{\Delta t}}$ ………..(3)
It is clear from equation (1) and (2), that momentum varies linearly with respect to velocity. And we know that the graph between two linearly varying quantities is a ‘straight line passing through the origin’. While the slope of the graph depends upon the mass of the body.

So, (C) option is correct.

Note: It is important to note that momentum is that, for a closed system, the total momentum is constant. This is 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.