The SI unit of G is

Options

A. `N^(2)-m^(2)//kg`
B. `N-m^(2)//kg`
C. `N-m//kg`
D. `N-m^(2)//kg^(2)`

Explanation

To find the SI unit of the universal gravitational constant \( G \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Law of Gravitation**: According to Newton's Law of Gravitation, the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by:
\[ F \propto \frac{m_1 m_2}{r^2} \]

2. **Convert Proportionality to Equation**: To convert the proportionality into an equation, we introduce a constant \( G \):
\[ F = G \frac{m_1 m_2}{r^2} \]

3. **Rearranging for \( G \)**: Rearranging the equation to solve for \( G \):
\[ G = \frac{F r^2}{m_1 m_2} \]

4. **Identify Units**: Now, we need to identify the units of each term in the equation:
- The unit of force \( F \) is Newton (N).
- The unit of distance \( r \) is meter (m), so \( r^2 \) will be in square meters (m²).
- The unit of mass \( m_1 \) and \( m_2 \) is kilogram (kg).

5. **Substituting Units into the Equation**: Substitute the units into the equation for \( G \):
\[ G = \frac{\text{N} \cdot \text{m}^2}{\text{kg} \cdot \text{kg}} = \frac{\text{N} \cdot \text{m}^2}{\text{kg}^2} \]

6. **Final Unit of \( G \)**: Therefore, the SI unit of the universal gravitational constant \( G \) is:
\[ G = \text{N} \cdot \text{m}^2/\text{kg}^2 \]

### Final Answer:
The SI unit of \( G \) is \( \text{N} \cdot \text{m}^2/\text{kg}^2 \).

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