Question

Consider a collection of a large number of particles moving with the same speed v in random directions. Could you, by using simple logic, show that the magnitude of the relative velocity of a pair of particles averaged over all the pairs of the collection is greater than v ?

Answer 1

In other words between 0 and 60 the relative velocity is less than v, while between 60 and 180 it is greater than v. Hence the relative velocity averaged over all directions