Which of the following quantity is direction less

Options

A. moment of momentum
B. Moment of force
C. Moment of charge
D. Moment of inertia

Answer

To determine which of the following quantities is directionless, we will analyze each option given in the question.

### Step 1: Analyze Moment of Momentum
- **Definition**: Moment of momentum, also known as angular momentum, is a measure of the rotational motion of an object.
- **Direction**: It has a direction associated with the axis of rotation and the direction of the motion. Therefore, it is a vector quantity.

### Step 2: Analyze Moment of Force
- **Definition**: Moment of force, or torque, is the measure of the force causing an object to rotate about an axis.
- **Direction**: Torque has a direction based on the axis of rotation and the direction of the applied force. Thus, it is also a vector quantity.

### Step 3: Analyze Moment of Charge
- **Definition**: The moment of charge is associated with an electric dipole moment, which describes the separation of positive and negative charges.
- **Direction**: This quantity also has a direction, as it is defined in terms of the orientation of the dipole. Hence, it is a vector quantity.

### Step 4: Analyze Moment of Inertia
- **Definition**: Moment of inertia is a scalar quantity that measures how difficult it is to change the rotational motion of an object.
- **Direction**: It is calculated as I = m * r², where m is mass and r is the distance from the axis of rotation. Since it does not have a directional component, it is directionless.

### Conclusion
After analyzing all the options, we find that the only quantity that is directionless is the **moment of inertia**.

**Final Answer**: Moment of Inertia

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