Statement-I : Magnitude of torque of a force about a given point does not depend upon the location of the origin of the co-ordinate system.
Statement II: Moment of couple is different for different points in its plane

Options

A. Statement-I is True, Statement-II is True and Statement-II is a correct explanation for Statement-I
B. -I is True, Statement-II is True and 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 solve the problem, we need to analyze both statements provided:

**Statement I**: The magnitude of torque of a force about a given point does not depend upon the location of the origin of the coordinate system.

**Statement II**: The moment of a couple is different for different points in its plane.

### Step-by-Step Solution:

**Step 1: Understanding Torque**
- Torque (\( \tau \)) is defined as the cross product of the position vector (\( \mathbf{R} \)) from the point of rotation to the point of application of the force (\( \mathbf{F} \)).
- The formula for torque is given by:
\[ \tau = \mathbf{R} \times \mathbf{F} \]

**Step 2: Analyzing Statement I**
- Let’s consider a point \( O \) and a point \( P \) where the force \( \mathbf{F} \) is applied.
- The position vector \( \mathbf{R} \) from point \( O \) to point \( P \) is denoted as \( \mathbf{R} = \mathbf{r} \hat{r} \).
- The magnitude of the torque can be expressed as:
\[ |\tau| = |\mathbf{R}| |\mathbf{F}| \sin(\theta) \]
where \( \theta \) is the angle between \( \mathbf{R} \) and \( \mathbf{F} \).

**Step 3: Conclusion for Statement I**
- The torque depends on the relative position of the force and the point about which it is calculated, not on the choice of the origin of the coordinate system.
- Therefore, **Statement I is true**.

**Step 4: Analyzing Statement II**
- A couple consists of two equal and opposite forces acting on an object, separated by a distance \( d \).
- The torque due to a couple is given by:
\[ \tau = F \cdot d \]
where \( F \) is the magnitude of one of the forces and \( d \) is the perpendicular distance between the lines of action of the forces.

**Step 5: Conclusion for Statement II**
- The torque due to a couple is constant regardless of the point about which it is calculated. It does not change with the choice of point in the plane of the couple.
- Therefore, **Statement II is false**.

### Final Conclusion:
- **Statement I is true**: The magnitude of torque does not depend on the location of the origin.
- **Statement II is false**: The moment of a couple is the same for all points in its plane.