For a completely inelastic collision of two particles in one dimension, which of the following statements are correct.a)The kinetic energy is conservedb)The linear momentum is coveredc)The particles move with a common velocity after the collision.d)The total energy is conserved.Correct answer is option 'B,C,D'. Can you explain this answer?

Question

Answer

Understanding Completely Inelastic Collisions
In a completely inelastic collision, two particles collide and stick together, moving as a single entity post-collision. Let's analyze the statements regarding the conservation laws involved in such a scenario.
Conservation of Kinetic Energy
- In a completely inelastic collision, kinetic energy is not conserved.
- Some kinetic energy is transformed into other forms of energy, such as heat and sound, during the collision.
Conservation of Linear Momentum
- Linear momentum is conserved in all types of collisions, including completely inelastic ones.
- The total momentum before the collision equals the total momentum after the collision, represented by the equation: m1u1 + m2u2 = (m1 + m2)v, where v is the common velocity after the collision.
Common Velocity After Collision
- In a completely inelastic collision, the two particles move with a common velocity after the collision.
- This results from them sticking together, indicating they share the same final velocity.
Total Energy Conservation
- While kinetic energy is not conserved, the total energy (including potential energy and internal energy) of the system is conserved.
- This means that while some of the kinetic energy is lost, the overall energy remains constant.
Conclusion
Thus, the correct statements regarding a completely inelastic collision are:
- B: Linear momentum is conserved.
- C: The particles move with a common velocity after the collision.
- D: Total energy is conserved.
This analysis reveals the fundamental differences between kinetic energy and momentum conservation in inelastic collisions.

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