Question

The physical quantity which is equal to the rate of change of momentum is_________?
(A) Displacement
(B) Acceleration
(C) Force
(D) Impulse

Answer 1

We have to start with the definition of momentum and we need to differentiate both sides of the momentum equation.

Complete step by step answer:
As per Newton’s second law, the rate of change of momentum is equal to the force applied.
The change in momentum of an object is its times the change in its velocity.

$$p = mv \\\ \dfrac{{dp}}{{dt}}{\text{ }} = {\text{ }}m.\left( {\dfrac{{dv}}{{dt}}} \right){\text{ + v}}{\text{.}}\left( {\dfrac{{dm}}{{dt}}} \right){\text{ }} \\\$$

For a constant mass,
$\dfrac{{dm}}{{dt}} = 0$

$$\dfrac{{dp}}{{dt}} = m.\dfrac{{dv}}{{dt}} \\\ \dfrac{{dp}}{{dt}} = {\text{ }}m.\left( {{v_f} - {v_i}} \right) \\\ \dfrac{{dp}}{{dt}} = ma = F \\\$$

If a force $F$ acts on an object for a time $\Delta t$, the change in the object’s momentum is $\Delta p = F\Delta t.$
Hence the correct answer is force. $\left( C \right).$

Note: We can use dimension analysis instead of this method.
A force is a push on pull upon an object resulting from the object’s interaction with another object whenever there is an interaction between two objects, there is a force upon each of the objects. The SI unit of force is the newton, $N$.