Which of the following physical quantities has neither dimensions nor unit ?

Options

A. Angle
B. Luminous intensity
C. Coefficient of friction
D. Current

Answer

To solve the question of which physical quantity has neither dimensions nor units, we can analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding Physical Quantities**:
- Physical quantities can be classified based on whether they have dimensions and units.
- A dimensionless quantity is one that does not depend on any physical dimensions (length, mass, time, etc.) and thus has no units.

2. **Analyzing the Options**:
- **Option 1: Angle**
- An angle (θ) is defined as the ratio of arc length (l) to radius (r): θ = l/r.
- Since both l and r have dimensions of length, they cancel out, making θ dimensionless.
- However, angles do have a unit (radian), so this option is incorrect.

- **Option 2: Luminous Intensity**
- Luminous intensity is one of the seven fundamental quantities.
- It has a dimension and its unit is candela (cd).
- Therefore, this option is incorrect.

- **Option 3: Coefficient of Friction (μ)**
- The coefficient of friction is defined as the ratio of the frictional force (F) to the normal force (N): μ = F/N.
- Since both F and N are forces, they have the same dimension and cancel out, making μ dimensionless.
- Additionally, the coefficient of friction does not have a unit, so this option is correct.

- **Option 4: Current**
- Electric current is a fundamental quantity with a dimension.
- Its unit is ampere (A). Thus, this option is incorrect.

3. **Conclusion**:
- The only physical quantity among the options that has neither dimensions nor units is the **coefficient of friction**.

### Final Answer:
The correct answer is the **coefficient of friction**.