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

Options

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

Answer

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

### Step 1: Identify the SI units of \( g \) and \( G \)
- The acceleration due to gravity \( g \) has the SI unit of meters per second squared, which is written as \( \text{m/s}^2 \).
- The gravitational constant \( G \) is defined through the formula for gravitational force:
\[ F = \frac{G m_1 m_2}{r^2} \]
where \( F \) is in newtons (N), \( m_1 \) and \( m_2 \) are masses in kilograms (kg), and \( r \) is the distance in meters (m).

### Step 2: Express the unit of \( G \)
- We know that 1 newton (N) is equal to \( 1 \, \text{kg} \cdot \text{m/s}^2 \).
- Rearranging the formula for \( G \):
\[ G = \frac{F r^2}{m_1 m_2} \]
- The units of \( G \) can be derived as follows:
\[ \text{Unit of } G = \frac{\text{N} \cdot \text{m}^2}{\text{kg} \cdot \text{kg}} = \frac{(\text{kg} \cdot \text{m/s}^2) \cdot \text{m}^2}{\text{kg}^2} = \frac{\text{kg} \cdot \text{m}^3}{\text{s}^2 \cdot \text{kg}^2} = \frac{\text{m}^3}{\text{s}^2 \cdot \text{kg}} \]

### Step 3: Write the expression for \( \frac{g}{G} \)
- Now we can express \( \frac{g}{G} \):
\[ \frac{g}{G} = \frac{\text{m/s}^2}{\frac{\text{m}^3}{\text{s}^2 \cdot \text{kg}}} \]

### Step 4: Simplify the expression
- When we divide \( g \) by \( G \):
\[ \frac{g}{G} = \frac{\text{m/s}^2 \cdot \text{s}^2 \cdot \text{kg}}{\text{m}^3} = \frac{\text{kg}}{\text{m}^2} \]

### Step 5: Conclusion
- Therefore, the SI unit of the quantity \( \frac{g}{G} \) is \( \frac{\text{kg}}{\text{m}^2} \).

### Final Answer:
The unit of the quantity \( \frac{g}{G} \) in SI will be \( \text{kg/m}^2 \).

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