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

Options

A. Total kinetic energy
B. Total mechanical energy
C. Total linear momentum
D. Speed of each body

Explanation

To solve the question regarding which quantities remain conserved during an inelastic collision between two bodies, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Inelastic Collision**:
- In an inelastic collision, two bodies collide and stick together or deform, resulting in a loss of kinetic energy. However, momentum is still conserved.

**Hint**: Remember that inelastic collisions involve a loss of kinetic energy, but momentum conservation is a key principle.

2. **Identify the Quantities**:
- The quantities we need to consider are:
- Kinetic Energy
- Total Mechanical Energy (which includes both kinetic and potential energy)
- Total Linear Momentum

**Hint**: List the quantities that could potentially be conserved and analyze each one based on the nature of inelastic collisions.

3. **Kinetic Energy Conservation**:
- In inelastic collisions, kinetic energy is not conserved. Some of the kinetic energy is transformed into other forms of energy, such as heat or sound.

**Hint**: Recall that inelastic collisions are characterized by a loss of kinetic energy.

4. **Total Mechanical Energy Conservation**:
- Since kinetic energy is not conserved in an inelastic collision, the total mechanical energy (which includes kinetic and potential energy) is also not conserved.

**Hint**: Mechanical energy conservation is tied to kinetic energy conservation; if one is not conserved, the other cannot be either.

5. **Total Linear Momentum Conservation**:
- The total linear momentum of the system (the two bodies) before and after the collision remains conserved. This is a fundamental principle of physics that applies to all types of collisions, including inelastic ones.

**Hint**: Momentum conservation is a universal law in physics, applicable regardless of whether the collision is elastic or inelastic.

6. **Conclusion**:
- Therefore, the only quantity that remains conserved during an inelastic collision between two bodies is the **total linear momentum**.

### Final Answer:
The quantity that always remains conserved during an inelastic collision between two bodies is **total linear momentum**.