Question

A 5-kg ball collides inelastically head-on with a 10-kg ball, which is initially stationary. Which of the following statements is true?

The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball.
Both balls lose all their momentum since the collision is inelastic.
The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball.
The magnitude of the change of velocity the 5-kg ball experiences is equal to that of the 10-kg ball.
The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball.

Answer 1

The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball.

Step-by-step explanation:

In inelastic collision, the total momentum is always conserved after collision but the kinetic energy is reduced.

Momentum is Mass X velocity.

5 kg ball is in motion, while 10 kg ball is stationary; that is zero velocity.

The momentum of 10 kg ball before collision is zero while the momentum of 5 kg ball before collision is more than zero. Therefore, the magnitude of change in momentum will not be equal.

Next possible options are in kinetic Energy

Initial Kinetic energy =
`(1)/(2)mu^2`

Final kinetic energy =
`(1)/(2)mv^2`

Change in kinetic energy = Final Kinetic Energy - Initial Kinetic Energy

Change in kinetic energy of 5kg ball =
`(1)/(2)mv^2 -(1)/(2)mu^2 = (1)/(2)m(v-u)^2`

Since the 5-kg ball has initial velocity (u), the magnitude of the change in velocity will be reduced.

Change in kinetic energy of 10kg ball:

the ball is initially at rest, therefore the initial velocity (u) will be zero (0)

Δ K.E =
`(1)/(2)mv^2 -(1)/(2)mu^2 = (1)/(2)m(v-u)^2 = (1)/(2)m(v-0)^2 = (1)/(2)mv^2`

From the solution above, the magnitude of the change in velocity experienced by 10 kg ball is higher than 5 kg ball.

Hence, The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball