# A particle of mass #m# moving with speed #v# hits elastically another stationary particle of mass #2m# inside a smooth horizontal circular tube of radius #r#. The time after which the second collision will happen?

##### 1 Answer

The circumference of the circle is

#### Explanation:

The momentum before the collision will be

Call the velocity of the particle of mass

We can cancel out

Since the collision is elastic, kinetic energy is conserved in the collision

Canceling out

The two equations can be rewritten in the form

Dividing both sides of the second equation by

gives

(Note that the last equation could have been directly obtained by using the alternative definition of elastic collisions - relative speed of approach equals that of separation - that would considerably shorten the answer!)

This implies that the relative speed of separation of the two objects is

When the two bodies collide again, the distances traveled by them must differ by

The time taken for this must be