If G is universal gravitational constant and g is acceleration due to gravity then the unit of the quantity `(G)/(g)` is

Options

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

Explanation

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

### Step 1: Understand the definitions
- \( G \) is the universal gravitational constant, which has a value of \( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \).
- \( g \) is the acceleration due to gravity, which has units of \( \text{m/s}^2 \).

### Step 2: Write down the units of \( G \) and \( g \)
- The unit of \( G \) is \( \text{N m}^2/\text{kg}^2 \).
- The unit of \( g \) is \( \text{m/s}^2 \).

### Step 3: Convert the unit of \( G \)
We know that \( 1 \, \text{N} = 1 \, \text{kg m/s}^2 \). Therefore, we can rewrite the unit of \( G \):
\[ G = 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 = 6.674 \times 10^{-11} \, \frac{\text{kg m}}{\text{s}^2} \cdot \frac{\text{m}^2}{\text{kg}^2} = 6.674 \times 10^{-11} \, \frac{\text{m}^2}{\text{s}^2 \cdot \text{kg}} \]

### Step 4: Calculate the units of \( \frac{G}{g} \)
Now, we can find the units of \( \frac{G}{g} \):
\[ \frac{G}{g} = \frac{\text{N m}^2/\text{kg}^2}{\text{m/s}^2} \]
Substituting the unit of \( g \):
\[ \frac{G}{g} = \frac{\text{N m}^2/\text{kg}^2}{\text{m/s}^2} = \frac{\text{N m}^2}{\text{kg}^2} \cdot \frac{s^2}{\text{m}} = \frac{\text{N m}}{\text{kg}^2} \cdot s^2 \]

### Step 5: Simplify the units
Now we can simplify \( \frac{\text{N m}}{\text{kg}^2} \):
\[ \frac{\text{N m}}{\text{kg}^2} = \frac{\text{kg m/s}^2 \cdot \text{m}}{\text{kg}^2} = \frac{\text{kg m}^2}{\text{kg}^2 \cdot s^2} = \frac{m^2}{kg \cdot s^2} \]

### Final Result
Thus, the unit of the quantity \( \frac{G}{g} \) is:
\[ \frac{G}{g} = \frac{m^2}{kg} \]