Understanding Perfectly Inelastic Collisions
In a perfectly inelastic collision, two objects collide and stick together, moving as a single object after the collision. This type of collision is characterized by the coefficient of restitution (e).
Coefficient of Restitution (e)
- The coefficient of restitution is defined as the ratio of the relative velocity of separation to the relative velocity of approach.
- Mathematically, it is expressed as:
e = (Velocity after collision) / (Velocity before collision)
Value of e in Different Collisions
- e = 1: This represents a perfectly elastic collision where kinetic energy is conserved.
- e = 0: This indicates a perfectly inelastic collision where the maximum kinetic energy is lost and the objects stick together.
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Why e = 0 for Perfectly Inelastic Collisions?
- In a perfectly inelastic collision, after the collision, the two objects move with a common velocity.
- Since they stick together and do not separate, the relative velocity of separation is zero.
- Therefore, the equation simplifies to e = 0, confirming that no kinetic energy is preserved in the form of relative motion after the collision.
Conclusion
For a perfectly inelastic collision, the value of the coefficient of restitution is 0, making option 'D' the correct answer. This indicates that the two objects have lost all their relative motion and are now moving together as one.