Which of the following is a dimensional constant?

Options

A. Magnification
B. Relative density
C. Gravitational constant
D. Relative error

Answer

To determine which of the given options is a dimensional constant, we first need to understand what a dimensional constant is. A dimensional constant is a physical quantity that has dimensions (units) associated with it, and its value remains constant.

### Step-by-Step Solution:

1. **Understanding Dimensional Constants**:
- A dimensional constant is a quantity that has both a fixed value and dimensions. This means it can be expressed in terms of fundamental quantities like mass (M), length (L), time (T), etc.

2. **Analyzing the Options**:
- We need to evaluate each option provided in the question to see if it qualifies as a dimensional constant.

3. **Option 1: Magnification**:
- Magnification is defined as the ratio of the image distance (V) to the object distance (U).
- Magnification = V/U
- Since it is a ratio of two lengths, it is dimensionless (no dimensions) and does not have a constant value.
- **Conclusion**: Not a dimensional constant.

4. **Option 2: Relative Density**:
- Relative density (or specific gravity) is the ratio of the density of a substance to the density of a reference substance (usually water).
- It is also dimensionless because it is a ratio of two densities.
- **Conclusion**: Not a dimensional constant.

5. **Option 3: Gravitational Constant (G)**:
- The gravitational constant (G) appears in Newton's law of gravitation and has a fixed value of approximately 6.67 × 10^-11 N(m/kg)^2.
- It has dimensions: [G] = M^-1 L^3 T^-2 (derived from the formula F = G(m1*m2)/r^2).
- Since G has dimensions and a constant value, it qualifies as a dimensional constant.
- **Conclusion**: This is a dimensional constant.

6. **Option 4: Relative Terms**:
- Any relative term, like relative velocity or relative density, is dimensionless.
- Since it lacks dimensions, it cannot be a dimensional constant.
- **Conclusion**: Not a dimensional constant.

### Final Answer:
The correct answer is **Option 3: Gravitational Constant (G)**, as it has dimensions and a constant value.

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