A particle of mass m collides with another stationary...

A particle of mass $m$ collides with another stationary particle of mass $M$. If the particle $m$ stops just after collision, the coefficient of restitution for collision is equal to
(a) 1
(b) $\frac{m}{M}$
(c) $\frac{M-m}{M+m}$
(d) $\frac{m}{M+m}$

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Key Concepts

Relative Velocity

Relative velocity in the context of collisions refers to the velocity of one object as observed from the frame of reference of another. It is essential to correctly applying the definition of the coefficient of restitution, as it involves comparing the speeds of the bodies involved both before and after the collision to understand the dynamics of their interaction.

Coefficient of Restitution

The coefficient of restitution is a measure of how elastic a collision is, defined as the ratio of the relative speed after collision (separation speed) to the relative speed before collision (approach speed). It determines how much kinetic energy is conserved during the collision and varies from 0 for a perfectly inelastic collision to 1 for a perfectly elastic collision.

Conservation of Momentum

Conservation of momentum is a fundamental principle in mechanics stating that the total momentum of a system remains constant in the absence of external forces. In collision problems, this law is used to relate the masses and velocities of the particles before and after the impact, providing a key equation for solving variables such as final velocities.

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