The change of momentum in each ball of mass 60gm , moving in opposite directions with speeds 4m / s collide and rebound with the same speed, is

Correct Option: The correct answer is 0.48 kg-m / s.

To find the change in momentum of each ball, we use the definition of momentum and vector velocity.

1. Identify the Given Parameters:
Mass of each ball, $m=60\text{gm}=60\times {10}^{-3}\text{kg}=0.06\text{kg}$
Initial speed of each ball, $u=4\text{m/s}$

2. Define Velocity Vectors:
Let us consider the motion along a straight line (the x-axis). Since the two balls are moving in opposite directions, we can assign positive and negative directions to their velocities.
For one of the balls:
Initial velocity, $v_i=+4\text{m/s}$
Since the ball rebounds with the same speed in the opposite direction after the collision:
Final velocity, $v_f=-4\text{m/s}$

3. Calculate Initial and Final Momentum:
Initial momentum:
$p_i=m\times v_i=0.06\text{kg}\times 4\text{m/s}=0.24\text{kg-m/s}$
Final momentum:
$p_f=m\times v_f=0.06\text{kg}\times (-4\text{m/s})=-0.24\text{kg-m/s}$

4. Calculate the Change in Momentum:
The change in momentum ($\Delta p$) is given by the difference between the final momentum and the initial momentum:
$\Delta p=p_f-p_i$
$\Delta p=-0.24\text{kg-m/s}-0.24\text{kg-m/s}=-0.48\text{kg-m/s}$

Taking the magnitude of this change:
$\left|\Delta p\right|=0.48\text{kg-m/s}$

Thus, the magnitude of the change of momentum in each ball is 0.48 kg-m / s.