During inelastic collision between two bodies, which of the following quantities always remain conserved?

The correct option is Total linear momentum.

To understand why total linear momentum always remains conserved during an inelastic collision, let us break down the physical concepts involved step-by-step:

1. Definition of a Collision and External Forces:
During any collision between two bodies, the forces acting between the colliding bodies are internal forces. If there is no net external force acting on the system of two bodies, the system is considered isolated.

2. Conservation of Linear Momentum:
According to Newton's second law of motion, the net external force acting on a system is equal to the rate of change of its total linear momentum:
$F=\frac{dp}{dt}$
When the net external force ($F$) is zero:
$\frac{dp}{dt}=0$
This implies that the total linear momentum ($p$) of the system remains constant (conserved) before, during, and after the collision. This conservation law holds true for all types of collisions, whether elastic or inelastic.

3. Why other quantities are not conserved:
• Total kinetic energy: In an inelastic collision, a portion of the initial kinetic energy is converted into other forms of energy, such as heat, sound, or vibrational energy, and is used in causing permanent deformation of the bodies. Therefore, kinetic energy is not conserved.
• Total mechanical energy: Since some kinetic energy is lost to non-mechanical forms of energy (like heat and sound), the total mechanical energy (kinetic energy + potential energy) of the system is not conserved.
• Speed of each body: The velocities and speeds of the individual bodies change as they exert forces on each other to redistribute momentum, so the speed of each body is not conserved.