Question

Impulse is equal to
A) Momentum
B) Change in momentum
C) Rate of change of momentum
D) Rate of change of force

Answer 1

Hint: This problem can be solved by combining the formulae for the force on a body in terms of the change in momentum in a time period and the impulse on a body in terms of the force on it and the time period that the force acts on. By doing this, we will get the required relation of impulse with momentum.

Formula used:
$F=\dfrac{\Delta p}{t}$
$J=Ft$

Complete step by step answer:
Let us use the formula for the force on a body in terms of the change in its momentum in a time period.
The magnitude of force $F$ acting on a body for a time period $t$ can be written as
$F=\dfrac{\Delta p}{t}$ --(1)
Where $\Delta p$ is the change in momentum of the body due to the action of that force.
Now, let us write the formula for the impulse on a body in terms of the force on it and the time period for which it acts.
The impulse $J$ on a body due to the application of a force $F$ on it for a time period $t$ is given as
$J=Ft$
$\therefore F=\dfrac{J}{t}$ --(2)
Putting (2) in (1), we get
$\dfrac{J}{t}=\dfrac{\Delta p}{t}$
$\therefore J=\Delta p$
Hence, we have got the relation that the impulse on a body is equal to its change in momentum.

Therefore, the correct option is B) Change in momentum.

Note:
Students sometimes get confused between the terms jerk and impulse. However, they must remember that impulse is the change in momentum, that is, it considers the mass of the body. However, jerk is only the rate of change of acceleration of the body and the mass of the body does not come into the picture in its mathematical expression.