Elastic And Inelastic Collisions

A collision in which kinetic energy remains conserved is called an elastic collision. In such a collision, both the total linear momentum and total kinetic energy of the system before and after the collision remain the same.
In contrast, in an inelastic collision, only momentum is conserved, while kinetic energy is partially or fully converted into other forms of energy (like heat, sound, or deformation energy).
Therefore, if the kinetic energy remains constant, the collision must be elastic.

Using the principle of conservation of momentum, the velocity of the bullet just before the collision is related to the velocity of the combined block and bullet system after collision. The block with mass and bullet with mass move together after collision. The potential energy of the block after the collision is given by: The kinetic energy of the bullet before the collision is related to the velocity as: By equating the kinetic and potential energies, we get: Thus: So the correct answer is (C).