Question

Which among the following options is equal to the impulse of a body?
A. Rate of change of its momentum
B. Change in its momentum
C. The product of force applied on it & the time of application of the force
D. Both B & C

Answer 1

Hint: First, try to understand the concept of impulse & then try to develop some mathematical relation between impulse, force & momentum.

Complete step by step answer:
We will first try to understand what exactly is meant by impulse & then we will come up with some mathematical relation to support our answer.
So, Impulse is a certain amount of force you apply for a certain amount of time to cause a change in momentum. In classical mechanics, impulse is the integral of a force F over the time interval, t for which it acts. Since force is a vector quantity, impulse is also a vector quantity.
Impulse is denoted by I or J.
∴ Impulse, I = Fdt
Force = ma = ${\text{m}}\dfrac{{{\text{dv}}}}{{{\text{dt}}}}$

∴ I = Fdt

= ${\text{m}}\dfrac{{{\text{dv}}}}{{{\text{dt}}}} \times {\text{dt}}$

= mdv

= m(v₂ − v₁)

= mv₂ − mv₁

= final momentum − initial momentum

= P₂ − P₁

∴ Impulse is equal to change in its momentum.
also since Impulse, I = Fdt
Therefore, it is also equal to the product of the force applied on it & the time of application of the force.
∴ Correct answer D. Both B & C

Note: Impulse is not equal to momentum itself, rather it’s the increase or decrease of an object’s momentum. This is also known as Impulse-Momentum theorem.