Introduction:
In an inelastic collision, the objects involved collide and stick together, resulting in a loss of kinetic energy. In this type of collision, momentum is conserved, but kinetic energy is not conserved. This is due to the transfer of energy from kinetic energy to other forms of energy, such as heat or deformation.

Explanation:
To understand why momentum is conserved while kinetic energy is not conserved in an inelastic collision, let's break it down further:

Momentum:
- Momentum is a vector quantity that depends on an object's mass and velocity. It is given by the equation: momentum = mass x velocity.
- In a collision, the total momentum of the system before the collision is equal to the total momentum after the collision, as long as no external forces are acting on the system.
- The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces are acting on it.
- In an inelastic collision, the objects collide and stick together, resulting in a combined mass and velocity. The momentum of the system before and after the collision remains the same, as long as no external forces are present.

Kinetic Energy:
- Kinetic energy is the energy of an object due to its motion. It is given by the equation: kinetic energy = 0.5 x mass x velocity^2.
- In a collision, the total kinetic energy of the system before the collision is not necessarily equal to the total kinetic energy after the collision.
- In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or deformation. This results in a loss of kinetic energy.

Example:
To illustrate this, let's consider a simple example of two objects colliding inelastically:

- Object A has a mass of 2 kg and a velocity of 4 m/s.
- Object B has a mass of 3 kg and a velocity of -2 m/s (opposite direction).
- Before the collision, the total momentum is 2 kg x 4 m/s + 3 kg x (-2 m/s) = 8 kg·m/s - 6 kg·m/s = 2 kg·m/s.
- After the collision, the objects stick together and move with a combined mass of 2 kg + 3 kg = 5 kg.
- The velocity of the combined objects can be calculated using the conservation of momentum: 2 kg·m/s / 5 kg = 0.4 m/s.
- The initial kinetic energy of Object A is 0.5 x 2 kg x (4 m/s)^2 = 16 J.
- The initial kinetic energy of Object B is 0.5 x 3 kg x (-2 m/s)^2 = 6 J.
- After the collision, the total kinetic energy is 0.5 x 5 kg x (0.4 m/s)^2 = 0.4 J.
- As we can see, there is a loss of kinetic energy from 22 J (initial total kinetic energy) to 0.4 J (final total kinetic energy).

Conclusion:
In an inelastic collision, momentum is conserved because the total momentum before the collision is equal to the total momentum after the collision. However, kinetic energy is not conserved because

A is correct