Question

If two balls each of mass \[0.06kg\] moving in opposite directions with speed of \[4m{s^{ - 4}}\] collide and rebound with the same speed, then the impulse imparted to each ball due to other is:
A. \[0.48kgm{s^{ - 1}}\]
B. \[0.53kgm{s^{ - 1}}\]
C. \[0.8kgm{s^{ - 1}}\]
D. \[0.92kgm{s^{ - 1}}\]

Answer 1

Hint: Here the two balls are having the mass of moving and making collide off each other with some certain speed of and taking rebound with the same speed. Here the momentum will be transferred to each other, so if we find the change in momentum means, we can get the answer.

Complete step by step solution:
\[u\] is represents the first ball and We know the mass of the ball \[u\] is \[m(u) = 0.06kg\]
\[v\] is represents a second ball and we know the mass of the ball \[v\] is \[m(v) = 0.06kg\]
Velocity \[V = 4m/s\]
Rebound velocity is \[{V_r} = - 4m/s\]
We know already impulse=change in momentum
So the impulse \[ = m(u) - m(v)\]
\[ = 0.06 \times 4 - (0.06 \times - 4)\]
\[ = 0.48kgm/s\]
Hence Option (A) is correct.

Additional Information:
Momentum is a measure of mass in motion: how much mass is moving and how fast. It is commonly denoted by the letter p. The term "impulse" refers to the overall effect of a force acting over time. It is commonly abbreviated as J and measured in Newton seconds.

Note: One of the reasons why impulse is significant and effective is that forces are rarely consistent in the actual world. People and engines generate forces that build up over time from zero and vary based on a variety of circumstances. It would be difficult to directly calculate the overall influence of all of these forces. We multiply the force by the time when we calculate impulse. This is the same as calculating the area beneath a force-time curve. This is useful because the area of a complicated shape (varying force) may be computed just as quickly as the area of a basic rectangle (constant force).