The unit of the quantity g/G in SI will be

Options

A. `kgm^(-2)`
B. `mkg^(-2)`
C. `m^(2)kg^(-1)`
D. `kg^(2)m^(-1)`

Answer

To find the unit of the quantity \( \frac{g}{G} \) in SI units, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Variables**:
- \( g \) is the acceleration due to gravity, which has units of \( \text{m/s}^2 \).
- \( G \) is the universal gravitational constant, which has units of \( \text{N m}^2/\text{kg}^2 \).

2. **Express the Units**:
- The unit of \( g \) is:
\[ g = \text{m/s}^2 \]
- The unit of \( G \) is:
\[ G = \text{N m}^2/\text{kg}^2 = \frac{\text{kg} \cdot \text{m/s}^2 \cdot \text{m}^2}{\text{kg}^2} = \frac{\text{kg} \cdot \text{m}^2}{\text{s}^2 \cdot \text{kg}^2} = \frac{\text{m}^2}{\text{s}^2 \cdot \text{kg}} \]

3. **Calculate the Ratio \( \frac{g}{G} \)**:
- Now, we can find the ratio \( \frac{g}{G} \):
\[ \frac{g}{G} = \frac{\text{m/s}^2}{\frac{\text{m}^2}{\text{s}^2 \cdot \text{kg}}} \]
- This can be simplified:
\[ \frac{g}{G} = \text{m/s}^2 \cdot \frac{\text{s}^2 \cdot \text{kg}}{\text{m}^2} = \frac{\text{kg}}{\text{m}} \]

4. **Final Result**:
- Therefore, the unit of the quantity \( \frac{g}{G} \) in SI units is:
\[ \text{kg/m} \]

### Final Answer:
The unit of the quantity \( \frac{g}{G} \) in SI units is \( \text{kg/m} \).