Question

A ball of weight \[0.1{\text{ }}kg\] coming with speed \[30{\text{ }}m/s\;\] strikes with a bat and returns in opposite direction with speed \[40{\text{ }}m/s\], then the impulse is (Taking final velocity as positive)
A. $ - 0.1 \times \left( {40} \right) - 0.1 \times \left( {30} \right)$
B. $0.1 \times \left( {40} \right) - 0.1 \times \left( { - 30} \right)$
C. $0.1 \times \left( {40} \right) + 0.1 \times \left( { - 30} \right)$
D. $0.1 \times \left( {40} \right) - 0.1 \times \left( {20} \right)$

Answer 1

Hint: In this question, we are given the mass of the ball \[0.1{\text{ }}kg\] and its initial and final velocity where final velocity is positive in the opposite direction. Therefore, initial velocity will be negative. Apply the formula of impulse. ${\text{Impulse = change in momentum}}$

Formula used:
Impulse – In physics, impulse is a term used to describe the effect of force that acts over time to change an object's momentum.
\[J = \Delta P\]
$\Rightarrow J = mv - mu$
Here, $v = $ final velocity
$u = $ initial velocity

Complete step by step solution:
Given that, weight of the ball, \[m = 0.1{\text{ }}kg\]
Now, the ball strikes the bat with the speed \[30{\text{ }}m/s\;\] and at the speed of \[40{\text{ }}m/s\] returns back. According to the question, if velocity will be positive in the opposite direction. It implies that it would be negative in the real direction.
So, initial velocity of the ball, \[u = - 30{\text{ }}m/s\;\]
And the final velocity of the ball, \[v = 40{\text{ }}m/s\]

As we know, impulse is equal to the change in momentum and momentum is the product of mass and the velocity of the body. Also, change in momentum is the difference between final momentum and the initial momentum. Impulse will be,
\[J = \Delta P\]
$\Rightarrow J = mv - mu$
$\therefore J = 0.1 \times 40 - 0.1 \times ( - 30)\;$

Hence, option B is the correct answer.

Note: The concepts of Impulse and Momentum offer a third way to solve kinetics problems in dynamics. This method is known as the Impulse-Momentum Method, and it is based on the idea that the impulse exerted on a body over a given time is equal to the change in momentum of that body.