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.

• A

  $v$
• B

  $4v$
• Correct answer
  C

  $\frac{4v}{\pi }$
• D

  $4\pi v$

Hence, the correct answer is option: 'C'.