Question

The impulse of a body is equal to:
A. Rate of change of momentum
B. Change in its momentum
C. The product of force applied on it and the time of application of the force
D. Both B and C

Answer 1

Hint: Intuitively impulse means as to how much push or pull is felt/exerted by a body over an interval of time. This means that the impulse is proportional to force and time. Using Newton's Second Law we can see that it simplifies and gives us the information that it is just a change in momentum.

Complete step by step answer:
Momentum: If an object of mass ‘m’ is moving with velocity ‘v’ then it has momentum (p) in it. It is a product of mass and velocity.
S.I unit of momentum is $kg\,m/\sec $.
$\vec p = \,m\,\vec v$ …(1)
Force: When a force is applied on an object of mass ‘m’ and it is accelerated by ‘a’ $m/{s^2}$. It is a product of mass and acceleration. S.I. unit of force is Newton
$F = ma$
Both momentum and force are vector quantities.
Rate of change of momentum: It is Newton’s 2nd law of motion defining force.
$F = \frac{{dp}}{{dt}}$ …(2)
Change in its momentum (dp):
From (1)
dp=mdv
dv = final velocity - initial velocity.
It can also be defined as a product of mass and change in the velocities of an object.
The product of the force applied to it and the time of application of the force:
From equation (2)
$dp = \,F\,\Delta t$
It is equivalent to change in momentum.
So, option B and C both are saying the same things.
Impulse: When a large amount of force is applied for a very short interval of time. It is a product of force and time interval.
$I\, = F\,\Delta t\, = \,dp$
Hence D is the correct option.

Note: There is a huge difference between the rate of change in momentum and change in momentum. One must remember that the term “rate” means the change in a quantity over an interval of time. This idea is going to help throughout one's journey in Physics.