Statement-1: if there is no external torque on a body about its centre of mass, then the velocity of the center of mass remains constant.
Statement-2: The linear momentum of an isolated system remains constant.

Options

A. Statement I is True, Statement II is True, Statement ll is a correct explanation for Statement I.
B. Statement I is True, Statement II is True, Statement II is NOT a correct explanation for Statement I
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Explanation

To analyze the statements given in the question, we will break down the reasoning step by step.

### Step 1: Understanding Statement-1
Statement-1 claims that if there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.

**Analysis**:
- The absence of external torque implies that the angular momentum of the system is conserved. However, this does not directly imply that the center of mass will have a constant velocity.
- For the center of mass to have a constant velocity, the net external force acting on the system must be zero (according to Newton's first law).
- It is possible for there to be forces acting on the body that do not create a torque about the center of mass (for example, if the forces are directed through the center of mass). In such cases, the center of mass can still accelerate even though the torque is zero.

**Conclusion**: Statement-1 is false.

### Step 2: Understanding Statement-2
Statement-2 states that the linear momentum of an isolated system remains constant.

**Analysis**:
- An isolated system is defined as one that does not exchange matter or energy with its surroundings. This means that there are no external forces acting on the system.
- According to the law of conservation of momentum, if no external forces are acting on a system, the total linear momentum of that system remains constant.
- Since the linear momentum \( p \) is defined as the product of mass \( m \) and velocity \( v \) (i.e., \( p = mv \)), and since the mass of the system is constant, the velocity of the center of mass must also remain constant for the momentum to remain constant.

**Conclusion**: Statement-2 is correct.

### Final Conclusion
- Statement-1 is false.
- Statement-2 is true.

Thus, the correct answer is that Statement-1 is incorrect and Statement-2 is correct.