The total change in momentum of the particle of mass m that collides elastically with a vertical rigid wall perpendicularly from the left with velocity v is 2mv to the left (option B).
The total change in momentum is given by:
[tex] \Delta p = p_{f} - p_{i} [/tex]
In the initial state, the particle is moving to the right until it collides with the rigid wall, so:
[tex] p_{i} = mv [/tex]
In the final state, the particle moves backward after the collision with the wall, so:
[tex] p_{f} = -mv [/tex]
The minus sign is because it is moving in the negative x-direction (to the left)
Hence, the total change in momentum is:
[tex] \Delta p = -mv - mv = -2mv [/tex]
Therefore, the total change in momentum of the particle is 2mv to the left (option B).
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