Question

A molecule in a gas container hits the wall with speed v at an angle θ with the normal and rebounds with the same speed as shown in Figure. Which of the following statement is/are true?

• A. The momentum of the system is conserved in the collision.
• B. The momentum of the molecule before collision with the wall is equal to the momentum of the molecule after collision.
• C. The collision is elastic.
• D. The collision is inelastic.

Answer 1

Answer: (A), (C)

The correct options are
A The momentum of the system is conserved in the collision.
C The collision is elastic.

The system consists of the molecule and the wall. Let us assume that initially the wall is stationary so that its momentum and kinetic energy are both zero before the collision is P = 0 + mv, where m is the mass of the molecule. After the collision the wall acquires a recoil velocity, say, V and a recoil momentum MV where M is the mass of the wall. After the collision, the recoil momentum of the wall + momentum of the system is conserved. Notice that the momenta of outgoing and incoming molecules are not the same, their direction are different.
Since the wall is infinitely massive, the recoil momentum produces a negligible velocity so that the kinetic energy of the wall is negligible after the collision. Since the speed v of the molecule is the same before and after collision, its kinetic energy remains unchanged. Hence the total kinetic energy is also conserved.
Therefore, the collision is elastic. Remember, in an inelastic collision, although the total momentum is conserved, the total kinetic energy is not conserved, it decreases.
Hence the correct choice are (a) and (c).