Question

Consider a collection of a large number of particles each with speed $v$. The direction of velocity is randomly distributed in the collection. The magnitude of the relative velocity between a pair of particles averaged over all the pairs in the collection is

• A. greater than $v$
• B. less than $v$
• C. equal to $v$
• D. we cant say anything

Answer 1

The correct option is A greater than $v$

$v_{rel}=2vSin\frac{\theta }{2}<v_{rel}>=\frac{{\int }_0^{2\pi }2vSin\frac{\theta }{2}d\theta }{{\int }_0^{2\pi }d\theta }=\frac{4v}{\pi }$
Thus, it is greater than $v$.