The bob A will not rise after the collision. It will stay at rest because the collision is elastic. In an elastic collision, the velocities are interchanged. Hence, the bob A will come to rest and the bob B will move with the velocity of bob A after collision.
NOTE: Elastic collisions are collisions in which both momentum and kinetic energy are conserved. The total system kinetic energy before the collision equals the total system kinetic energy after the collision. If total kinetic energy is not conserved, then the collision is referred to as an inelastic collision.
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