The S.I. units of intensity of gravitational field

Options

A. `J//kg`
B. `J//kgs^(2)`
C. `N//kg`
D. `m//s^(3)`

Answer

To find the S.I. units of the intensity of the gravitational field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition**: The intensity of the gravitational field (often denoted as \( g \)) is defined as the gravitational force per unit mass. Mathematically, this can be expressed as:
\[ g = \frac{F}{m} \]
where \( F \) is the gravitational force and \( m \) is the mass.

2. **Identify the Units**:
- The unit of gravitational force \( F \) is Newton (N).
- The unit of mass \( m \) is kilogram (kg).

3. **Substituting the Units**:
Now, substituting the units into the formula for gravitational field intensity:
\[ g = \frac{\text{Newton}}{\text{kilogram}} = \frac{N}{kg} \]

4. **Express Newton in Base SI Units**:
We know that 1 Newton is defined as:
\[ 1 \, N = 1 \, kg \cdot m/s^2 \]
Thus, we can rewrite the unit of gravitational field intensity as:
\[ g = \frac{kg \cdot m/s^2}{kg} \]

5. **Simplifying the Expression**:
The kilograms in the numerator and denominator cancel out:
\[ g = \frac{m}{s^2} \]

6. **Final Result**:
Therefore, the S.I. unit of the intensity of the gravitational field is:
\[ g = \text{Newton per kilogram} \, (N/kg) \]

### Conclusion:
The correct answer is \( N/kg \) (Newton per kilogram), which is option number 3.