Assertion: If a projectile explodes in mid air, linear momentum of center of mass of different fragments remains constant. Reason: Center of mass in this case follows the same path.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct 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:

### Step 1: Understand the Assertion
The assertion states that if a projectile explodes in mid-air, the linear momentum of the center of mass of the different fragments remains constant.

**Hint:** Remember that the principle of conservation of momentum applies when there are no external forces acting on the system.

### Step 2: Analyze the Situation
When the projectile explodes, it breaks into several fragments. According to the law of conservation of momentum, the total momentum before the explosion must equal the total momentum after the explosion, provided no external forces act on the system.

**Hint:** Consider the momentum before and after the explosion. How does the absence of external forces affect the momentum?

### Step 3: Calculate Initial and Final Momentum
Let’s denote the initial momentum of the projectile before the explosion as \( p_{initial} = mv \), where \( m \) is the mass of the projectile and \( v \) is its velocity. After the explosion, the momentum of the fragments must equal the initial momentum, so \( p_{final} = p_{initial} \).

**Hint:** Think about how the momentum is distributed among the fragments after the explosion.

### Step 4: Understand the Reason
The reason states that the center of mass in this case follows the same path. This is true because the center of mass of a system continues to move in the same direction at the same velocity unless acted upon by an external force.

**Hint:** Reflect on the definition of the center of mass and how it behaves in a closed system.

### Step 5: Conclusion
Both the assertion and the reason are correct. The assertion is true because the linear momentum of the center of mass remains constant due to the conservation of momentum, and the reason is correct because the center of mass continues to follow the same path.

Thus, the correct answer is that both the assertion and reason are true, and the reason is the correct explanation of the assertion.

**Final Answer:** Option A is the correct answer.