Question

a particle of mass m moving with a speed v hits elastically another stationary particle of mass 2m on a smooth horizontal circular tube of radius R. find the time when the next collision will take place

Answer 1

The velocity of the particle of mass m after the collision can be called v1, and the velocity of the particle of mass 2m v2.

Thus, mv=mv1+2mv2

Eventually giving v=v1+2v2

12mv2=12mv21+122mv22

Eventually, it is

v2=v21+2v21

Dividing both sides of the second equation by v−v1 we get

v+v1=2v222v2=v2

Thus, the relative speed of separation of the two objects is
v2−v1=v

When the two bodies collide again, the distances travelled by them must differ by 2πr.

The time taken for this must be
t=2πrv2−v1
=2πrv


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Answer 2

A particle of mass m strikes elastically with a disc of radius R, with a velocity →v as shown. If the mass of the disc is equal to that of the ...