A dimensionless quantity

Options

A. Must not have a unit
B. May have a unit
C. May not have a unit
D. Must have a unit

Answer

### Step-by-Step Solution:

1. **Understanding Dimensionless Quantities**:
- A dimensionless quantity is defined as a quantity that does not have any physical dimensions associated with it. This means it cannot be expressed in terms of fundamental quantities such as mass (M), length (L), or time (T).

2. **Examples of Dimensionless Quantities**:
- Common examples include angles (measured in radians), strain, and coefficients of friction. For instance, the angle θ can be expressed as the ratio of the arc length to the radius, both of which are lengths, resulting in a dimensionless ratio.

3. **Units vs. Dimensions**:
- It is important to differentiate between units and dimensions. While dimensions are based on fundamental physical quantities, units are specific measures of these dimensions. A dimensionless quantity may have a unit (like radians for angles) or may not have a unit at all (like strain).

4. **Strain as a Dimensionless Quantity**:
- Strain is defined as the change in length divided by the original length (ΔL/L). Since both ΔL and L are lengths, the ratio is dimensionless. Therefore, strain does not have a unit.

5. **Conclusion**:
- A dimensionless quantity can exist without a unit, or it can have a unit depending on the context. It is essential to recognize that dimensionless quantities are significant in various fields of physics and engineering.