Two perfectly elastic particles A and B of equal masses...

Two perfectly elastic particles $A$ and $B$ of equal masses travelling along the line joining them with velocity 15 $\mathrm{ms}^{-1}$ and $10 \mathrm{~ms}^{-1}$ respectively collide. Their velocities after the elastic collision will be (in $\mathrm{ms}^{-1}$ ) respectively (a) 20 and 5 (b) 10 and 15 (c) 5 and 20 (d) 0 and 25

Two perfectly elastic particles $A$ and $B$ of equal masses travelling along the line joining them with velocity 15 $\mathrm{ms}^{-1}$ and $10 \mathrm{~ms}^{-1}$ respectively collide. Their velocities after the elastic collision will be (in $\mathrm{ms}^{-1}$ ) respectively
(a) 20 and 5
(b) 10 and 15
(c) 5 and 20
(d) 0 and 25

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Key Concepts

Elastic Collision

An elastic collision is one in which both momentum and kinetic energy are conserved. In such collisions, the objects involved rebound off each other without any loss of total kinetic energy, making the analysis of the final velocities straightforward using conservation principles.

Conservation of Linear Momentum

The conservation of linear momentum states that in an isolated system with no external forces, the total momentum before the collision is equal to the total momentum after the collision. This principle is used to relate the velocities and masses of the colliding particles before and after impact.

Conservation of Kinetic Energy

In perfectly elastic collisions, not only is momentum conserved, but the total kinetic energy of the system is conserved as well. This additional condition provides a second independent equation that is crucial for solving for the unknown final velocities of the colliding particles.

One-Dimensional Collision Analysis

In one-dimensional collisions, all motions occur along a single straight line, which simplifies the problem to scalar equations rather than vector equations. This simplification is particularly helpful when applying conservation laws to determine post-collision velocities.

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