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

Question

Accepted Answer

In an inelastic collision between two bodies, the correct answer is that linear momentum is always conserved. Let's explore why Option 3 is correct and why the other options are not.

1. **Explanation for Option 3 (Linear Momentum):**
   - In physics, the law of conservation of linear momentum states that if no external forces act on a system, the total linear momentum of the system remains constant. This principle holds true for all types of collisions, including inelastic collisions. During an inelastic collision, the colliding bodies may stick together or deform, and kinetic energy is not conserved. However, the total linear momentum before and after the collision remains the same, provided no external forces are acting on the system. This is because linear momentum is a vector quantity that depends on the mass and velocity of the bodies, and the internal forces during the collision do not affect the total momentum of the system.

2. **Why Option 1 (Kinetic Energy) is incorrect:**
   - In an inelastic collision, kinetic energy is not conserved. Some of the kinetic energy is transformed into other forms of energy, such as heat, sound, or deformation energy. This is why inelastic collisions are characterized by a loss of kinetic energy. The total kinetic energy after the collision is less than the total kinetic energy before the collision, making Option 1 incorrect.

3. **Why Option 2 (Mechanical Energy) is incorrect:**
   - Mechanical energy is the sum of kinetic and potential energy in a system. In an inelastic collision, while potential energy might not change significantly, the loss of kinetic energy means that the total mechanical energy is not conserved. Some of the mechanical energy is converted into other forms of energy, such as thermal energy or energy used in deforming the objects. Therefore, mechanical energy is not conserved in inelastic collisions, making Option 2 incorrect.

4. **Why Option 4 (Both Kinetic Energy and Linear Momentum) is incorrect:**
   - As explained earlier, kinetic energy is not conserved in inelastic collisions, while linear momentum is conserved. Since kinetic energy is not conserved, Option 4, which suggests that both kinetic energy and linear momentum are conserved, is incorrect.

In summary, during an inelastic collision, the only quantity that is always conserved is linear momentum, making Option 3 the correct answer.