Question

A body of mass \[5{\text{ }}kg\] undergoes a change in speed from \[20{\text{ }} to {\text{ }}0.20{\text{ }}m/s.\] The momentum of the body would
A. Increase by \[99{\text{ }}kg{\text{ }}m/s\]
B. decrease by \[99{\text{ }}kg{\text{ }}m/s\]
C. increase by \[101{\text{ }}kg{\text{ }}m/s\]
D. decrease by \[90{\text{ }}kg{\text{ }}m/s\]

Answer 1

Hint:
To solve this question, i.e., to find the momentum of the body. We will apply the formula of change in momentum of the body. For that we will use the given mass of the body, and for the change in velocity, we will use the initial as well as final velocity of the body given, then on putting all the values in the formula, we will get our required answer. Since, we are using the formula of ‘change’ in momentum, then the answer which we will get will be either in terms of increasing or decreasing.

Complete step by step solution:
We have been given that a body of mass \[5{\text{ }}kg\] undergoes a change in speed from \[20{\text{ }}to{\text{ }}0.20{\text{ }}m/s.\]We need to find the momentum of the body.
So, the given initial speed of the body, \[u{\text{ }} = {\text{ }}20\;m/s\]

And, the final speed of the body, \[v{\text{ }} = {\text{ }}0.20\;m/s\]

We know that the change in momentum, \[\Delta p{\text{ }} = {\text{ }}m\left( {v - u} \right)\]

On putting the values in the above formula, we get
\[\Delta p{\text{ }} = {\text{ }}\left( 5 \right) \times \left( {0.20 - 20} \right) = - 99\;kg\;m/s\]

So, the momentum of the body decreases by \[99\;kg\;m/s.\]

Thus, option (B) decreases by \[99{\text{ }}kg{\text{ }}m/s\] is correct.

Note:
In the question, we are given about the momentum, let us understand about that in detail. Momentum refers to the quantity of motion, i.e., if an object is in motion, then it has momentum. The change in momentum of an object is its mass times the change in its velocity, and it can also be found by considering the force acting on it.