Consider a collection of a large number of particles each moving with speed v . The direction of velocity is randomly distributed in the collection. Find the magnitude of the relative velocity between a pair of

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Quantrex Academy · Accepted Answer

Correct answer: C. (4v)/(π)

Consider any two particles whose velocity vector particles making angle

\theta

.

Relative velocity v_AB = v_A - v_B

⇒ {v}_{rel} = \left(\sqrt{v^{2} + v^{2} - 2v^{2 }\text{cos}\theta}\right)<br /><br />

⇒ {v}_{rel} = 2v

\text{sin}\dfrac{θ}{2}<br /><br />Average of

{v}_{rel} =

\dfrac{\mathop{∫}_{0}^{2\pi}{v}_{rel}\text{d}\theta}{\mathop{∫}_{0}^{2\pi}\text{d}\theta} = \dfrac{4v}{\pi}

Consider a collection of a large number of particles each moving...

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