Which of the following is a dimensional variable ?

Options

A. force
B. exponential e
C. angle
D. velocity of light in vacuum

Answer

To determine which of the given options is a dimensional variable, we need to analyze each option based on its dimensionality and whether it can vary.

### Step-by-step solution:

1. **Understanding Dimensional Variables**:
- A dimensional variable is a physical quantity that has dimensions (like length, mass, time, etc.) and can vary in value.

2. **Analyzing Each Option**:
- **Force**:
- Force is a physical quantity that has dimensions. Its dimensional formula is [M^1 L^1 T^-2].
- It can vary depending on the mass and acceleration applied.
- **Conclusion**: Force is a dimensional variable.

- **Exponential**:
- The term "exponential" usually refers to a mathematical function or constant (like e).
- It does not have dimensions and is not a variable in the physical sense.
- **Conclusion**: Exponential is not a dimensional variable.

- **Angle**:
- Angles are measured in radians or degrees, which are dimensionless quantities.
- Although angles can vary, they do not possess dimensions.
- **Conclusion**: Angle is not a dimensional variable.

- **Velocity of Light in Vacuum**:
- The speed of light is a constant value (approximately 3 x 10^8 m/s) and has dimensions of [L^1 T^-1].
- However, since it is a constant, it does not vary.
- **Conclusion**: Velocity of light in vacuum is a dimensional quantity but not a variable.

3. **Final Conclusion**:
- Among the options provided, **Force** is the only quantity that is both dimensional and variable.

### Final Answer:
**Force** is the dimensional variable.

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