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 particles averaged over all the pairs in the collection.

Question

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 particles averaged over all the pairs in the collection., v, 4 v, 4 v π, 4 π v

MARKS App · Accepted Answer

Consider any two particles whose velocity vector particles making angle θ . Relative velocity v AB = v A - v B ⇒ v rel = v 2 + v 2 - 2 v 2 cos θ ⇒ v rel = 2 v sin θ 2 Average of v rel = ∫ 0 2 π v rel d θ ∫ 0 2 π d θ = 4 v π

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