Assertion: Linear momentum is conserved in both elastic and inelastic collisions.
Reason: Total energy is conserved in all collisions.

Options

A. IF both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If assertion is false but reason is true

Explanation

To solve the question, we need to analyze the assertion and the reason given:

**Assertion:** Linear momentum is conserved in both elastic and inelastic collisions.
**Reason:** Total energy is conserved in all collisions.

### Step-by-Step Solution:

1. **Understanding the Assertion:**
- Linear momentum is defined as the product of an object's mass and its velocity.
- In both elastic and inelastic collisions, the total linear momentum of the system before the collision is equal to the total linear momentum after the collision.
- Therefore, the assertion is **true**.

2. **Understanding the Reason:**
- The reason states that total energy is conserved in all collisions.
- In elastic collisions, both momentum and kinetic energy are conserved.
- In inelastic collisions, while momentum is conserved, kinetic energy is not conserved (some kinetic energy is transformed into other forms of energy, such as heat or sound).
- However, the total energy (which includes all forms of energy) is conserved in both types of collisions.
- Thus, the reason is also **true**.

3. **Evaluating the Relationship:**
- The assertion claims that linear momentum is conserved due to the nature of collisions, while the reason states that total energy conservation applies to all collisions.
- The conservation of linear momentum is specifically due to the absence of external forces acting on the system, not solely because total energy is conserved.
- Therefore, while both the assertion and reason are true, the reason does not correctly explain the assertion.

4. **Conclusion:**
- The assertion is true, and the reason is true, but the reason is not the correct explanation for the assertion.

### Final Answer:
- The correct option is: **Both assertion and reason are true, but reason is not the correct explanation of assertion.**