Question

When a molecule of a gas collides with the wall of a container, it gets a rebound and the momentum transferred to the wall is equal to

Answer 1

Momentum

1. The momentum of a particle can be defined as the multiplication of the mass of the particle by its velocity.
2. The momentum of a system before and after collision remains constant.

Step 1: Calculation of the momentum before the collision

Momentum before the collision can be written as follows:

$p_1=mv$

Here, $p_1$ is the initial momentum, $m$ is the mass of the particle, and $v$ is the initial velocity of the particle.

Step 2: Calculation of the momentum after the collision

1. After the collision, the particle gets rebounded. Hence, the final velocity will be equal to the initial velocity of the particle.
2. Due to the rebound, the direction of the velocity becomes opposite. Hence, negative in sign.

$p_2=-mv$

Here, $p_2$ is the final momentum

Step 3: Calculation of the momentum transferred

Since the momentum is conserved, the momentum transferred to the wall will be equal to the change in momentum of the particle.

$$\begin{gathered} p=p_1-p_2 \\ p=mv-\left(-mv\right) \\ p=2mv \end{gathered}$$

Here, $p$ is the momentum transferred to the wall.

Therefore, the momentum transferred to the wall is $2mv$.