23P1Q10

10        A

Change in momentum per collision, \displaystyle \Delta p=2mv

Time interval between collisions for each molecule, \displaystyle \Delta t=\frac{2p}{v}

Force produced by each molecule, \displaystyle f=\frac{\Delta p}{\Delta t}=2mv\div \frac{2p}{v}=\frac{m{{v}^{2}}}{p}

Total average force, \displaystyle F=N\times f=N\times \frac{m{{v}^{2}}}{p}

COMMENT: It is unfortunate that p, which usual denotes momentum, is also the box’s length in this question. But you should be smart enough to not be confused by the setter.

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