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

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.

TestHub · Accepted Answer

Consider any two particles whose velocity vector particles making angle $θ$ .

Relative velocity v_AB= v_A- v_B

$\Rightarrow v_{rel} = (\sqrt{v^{2} + v^{2} - 2 v^{2} cos θ})$

$\Rightarrow v_{rel} = 2 v sin \frac{θ}{2}$

Average of $v_{rel} = \frac{\int_{0}^{2 π} v_{rel} d θ}{\int_{0}^{2 π} d θ} = \frac{4 v}{π}$

Physics - Kinematics Question with Solution | TestHub

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