Two particles of equal masses 4M are initially at rest. A particle of mass M moving at speed u collides elastically with one of the larger balls. How many collisions occur?

Engineering

Physics

Collision

Question

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This is a classic elastic collision problem involving multiple masses. Since all collisions are elastic and masses are related (4M and M), we analyze momentum and energy conservation.

Key concept: For elastic collisions between masses m₁ and m₂, velocities after collision are:

$v_{1} = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} u_{1} + \frac{2 m_{2}}{m_{1} + m_{2}} u_{2}$

$v_{2} = \frac{2 m_{1}}{m_{1} + m_{2}} u_{1} + \frac{m_{2} - m_{1}}{m_{1} + m_{2}} u_{2}$

The sequence is: mass M hits left 4M ball, then that ball hits the right 4M ball, then the right ball returns and hits the original M mass again. This results in three distinct collisions.

Final Answer: 3 collisions