In any kind of collision

Options

A. linear momentum is always conserved
B. kinetic energy is always conserved
C. both (a) and (b)
D. neither (a) nor (b)

Answer

To solve the question regarding the conservation of linear momentum in collisions, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Momentum**:
- Momentum (p) is defined as the product of mass (m) and velocity (v) of an object:
\[ p = mv \]
- In a system of particles, the total momentum is the vector sum of the momenta of all the particles.

2. **Law of Conservation of Momentum**:
- The law states that in the absence of external forces, the total momentum of a closed system remains constant.
- Mathematically, if two objects collide, the total momentum before the collision equals the total momentum after the collision:
\[ m_1v_1 + m_2v_2 = m_1v_3 + m_2v_4 \]
- Here, \(m_1\) and \(m_2\) are the masses of the two colliding objects, \(v_1\) and \(v_2\) are their velocities before the collision, and \(v_3\) and \(v_4\) are their velocities after the collision.

3. **Identifying External Forces**:
- During a collision, if no external forces are acting on the system, we can conclude that the momentum is conserved.
- If there are external forces, they can change the momentum of the system.

4. **Kinetic Energy Considerations**:
- While momentum is always conserved in collisions, kinetic energy is not necessarily conserved unless the collision is elastic.
- In inelastic collisions, some kinetic energy is transformed into other forms of energy (like heat or sound), and thus the total kinetic energy after the collision is less than before.

5. **Conclusion**:
- The question states that in any kind of collision, linear momentum is always conserved. This is true regardless of whether the collision is elastic or inelastic.
- Therefore, the answer to the question is: **Linear momentum is always conserved in any kind of collision**.

### Final Answer:
**Linear momentum is always conserved in any kind of collision.**

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