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 \(\frac{G}{g}\), where \(G\) is the universal gravitational constant and \(g\) is the acceleration due to gravity, we will follow these steps:

### Step 1: Identify the units of \(G\) and \(g\)

1. **Unit of \(G\)**: The universal gravitational constant \(G\) has the unit of \(\text{N m}^2/\text{kg}^2\) (Newton meter squared per kilogram squared).
- 1 Newton (N) = 1 kg m/s², so the unit of \(G\) can be expressed as:
\[ G = \frac{\text{kg} \cdot \text{m}^2}{\text{kg}^2} = \frac{\text{m}^2}{\text{kg} \cdot \text{s}^2} \]

2. **Unit of \(g\)**: The acceleration due to gravity \(g\) has the unit of \(\text{m/s}^2\).

### Step 2: Write the expression for \(\frac{G}{g}\)

Now we can express the quantity \(\frac{G}{g}\):
\[ \frac{G}{g} = \frac{\frac{\text{m}^2}{\text{kg} \cdot \text{s}^2}}{\frac{\text{m}}{\text{s}^2}} \]

### Step 3: Simplify the expression

To simplify \(\frac{G}{g}\), we multiply by the reciprocal of \(g\):
\[ \frac{G}{g} = \frac{\text{m}^2}{\text{kg} \cdot \text{s}^2} \cdot \frac{\text{s}^2}{\text{m}} = \frac{\text{m}^2 \cdot \text{s}^2}{\text{kg} \cdot \text{s}^2 \cdot \text{m}} = \frac{\text{m}}{\text{kg}} \]

### Step 4: Final unit of \(\frac{G}{g}\)

Thus, the unit of the quantity \(\frac{G}{g}\) is:
\[ \frac{G}{g} = \frac{\text{m}}{\text{kg}} \]

### Conclusion

The final answer is that the unit of the quantity \(\frac{G}{g}\) is \(\text{m/kg}\).

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