Question

Two particles with the same mass of 11 kg are involved in a completely inelastic head-on collision. Before the collision both particles have the same speed of 3 m/s. Which statement below describes the velocities of the particles after the collision? 

 One of the particles continues at 3 m/s, and the other reverses direction and moves at 6 m/s. 

 Each particle's speed is still 3 m/s, but each has reversed its direction. 

 There is not enough information to determine the velocities after the collision. 

One of the particles continues to move at 3 m/s, while the other particle is at rest. 

 Both particles have zero velocity.

Answer 1

Given Mass of the particles, \(m=3 \mathrm{~kg}\) Velocities of particle, \(v_{1}=3 \mathrm{~m} / \mathrm{s}\) and \(v_{2}=-3 \mathrm{~m} / \mathrm{s}\) Negative sign indicates the other particle is moving in the direction opposite to the first particle i.e., head on collision

Collisions conserve momentum. Momentum before collision

\(\begin{aligned} p_{i} &=m v_{1}+m v_{2} \\ &=m\left(v_{1}+v_{2}\right) \\ &=11(3+(-3)) \quad\left(\begin{array}{l}\text { negative sign indicates head on collision } \\ \text { 'opposite direction' }\end{array}\right)\\ &=11(0) \\ &=0 \end{aligned}\)

Momentum before collision = Momentum after collision

So, \(p_{f}=0\)

Since mass cannot be zero, the velocities of both the particles are zero.

Thus, the correct option is Both particles have zero velocity.