The SI unit of the universal gravitational constant G is

Options

A. Nm `kg^(–2)`
B. `Nm^(2)kg^(–2)`
C. `Nm^(2) kg^(–1)`
D. Nm`kg^(–1)`

Answer

To determine the SI unit of the universal gravitational constant \( G \), we can start from Newton's law of universal gravitation, which states that the force \( F \) between two point masses \( M_1 \) and \( M_2 \) separated by a distance \( R \) is given by:

\[ F = \frac{G \cdot M_1 \cdot M_2}{R^2} \]

### Step 1: Rearranging the equation
To find \( G \), we can rearrange the equation to solve for it:

\[ G = \frac{F \cdot R^2}{M_1 \cdot M_2} \]

### Step 2: Identifying the SI units
Now, we need to identify the SI units of each term in the equation:

- The SI unit of force \( F \) is the Newton (N).
- The SI unit of distance \( R \) is the meter (m).
- The SI unit of mass \( M_1 \) and \( M_2 \) is the kilogram (kg).

### Step 3: Substituting the units into the equation
Substituting the SI units into the equation for \( G \):

\[ G = \frac{\text{N} \cdot \text{m}^2}{\text{kg} \cdot \text{kg}} = \frac{\text{N} \cdot \text{m}^2}{\text{kg}^2} \]

### Step 4: Expressing Newton in base SI units
We know that 1 Newton (N) can be expressed in terms of base SI units as:

\[ 1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2 \]

### Step 5: Substituting Newton's unit into the equation
Now, substituting this into our equation for \( G \):

\[ G = \frac{(1 \text{ kg} \cdot \text{m/s}^2) \cdot \text{m}^2}{\text{kg}^2} = \frac{1 \text{ kg} \cdot \text{m}^3}{\text{kg}^2 \cdot \text{s}^2} \]

### Step 6: Simplifying the units
Now, simplifying the units gives us:

\[ G = \frac{1 \text{ m}^3}{\text{kg} \cdot \text{s}^2} \]

### Final Answer
Thus, the SI unit of the universal gravitational constant \( G \) is:

\[ \text{m}^3 \cdot \text{kg}^{-1} \cdot \text{s}^{-2} \]