Assertion : If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.
Reason : The linear momentum of an isolated system remains constant.

Options

A. If both, Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
B. If both, Assertion and Reason are true but Reason is not a correct explanation of the Assertion.
C. If Assertion is true but the Reason is false.
D. If both, Assertion and Reason are false.

Explanation

To solve the question regarding the assertion and reason, we will analyze both statements step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states: "If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant."
- This implies that for the velocity of the center of mass to remain constant, there should be no net external forces acting on the body.

2. **Analyzing the Condition of Torque**:
- Torque (\( \tau \)) is defined as \( \tau = R \times F \), where \( R \) is the position vector from the center of mass to the point of force application, and \( F \) is the force.
- If the force is applied at the center of mass, then \( R = 0 \), which means \( \tau = 0 \). Thus, there is no external torque.

3. **Considering External Forces**:
- Even if there is no external torque, if there is an external force acting on the body (for example, a force \( F \) applied at the center of mass), this will cause the body to accelerate.
- According to Newton's second law, \( F = ma \), where \( a \) is the acceleration. This means that the velocity of the center of mass will change, contradicting the assertion.

4. **Conclusion on the Assertion**:
- Since an external force can still act on the body even if there is no external torque, the assertion is **false**. The velocity of the center of mass does not remain constant if there is a net external force acting on it.

5. **Understanding the Reason**:
- The reason states: "The linear momentum of an isolated system remains constant."
- An isolated system is one where no external forces act. In such a case, the total linear momentum \( p = mv \) remains constant because both mass \( m \) and velocity \( v \) do not change.

6. **Analyzing the Reason**:
- If there are no external forces acting on the system, then the acceleration is zero, and thus the velocity of the center of mass remains constant.
- Therefore, the reason is **true**.

7. **Conclusion on the Reason**:
- While the reason is true, it does not explain the assertion correctly. The assertion is about the condition of torque and external forces affecting the velocity of the center of mass, while the reason pertains to the conservation of momentum in an isolated system.

### Final Answer:
- **Assertion**: False
- **Reason**: True
- The reason does not adequately explain the assertion.