The S.I. unit of gravitational potential is

Options

A. `J`
B. `J-kg^(-1)`
C. `J-kg`
D. `J-kg^(2)`

Answer

To determine the S.I. unit of gravitational potential, we can follow these steps:

### Step 1: Understand the Definition of Gravitational Potential
Gravitational potential at a point in a gravitational field is defined as the work done per unit mass to move an object from infinity to that point.

### Step 2: Write the Formula for Gravitational Potential
The formula for gravitational potential (V) can be expressed as:
\[ V = \frac{W}{m} \]
where:
- \( V \) is the gravitational potential,
- \( W \) is the work done,
- \( m \) is the mass of the object.

### Step 3: Identify the Units of Work Done
The S.I. unit of work done (W) is Joules (J).

### Step 4: Identify the Units of Mass
The S.I. unit of mass (m) is kilograms (kg).

### Step 5: Calculate the S.I. Unit of Gravitational Potential
Substituting the units into the formula for gravitational potential:
\[ \text{Unit of } V = \frac{\text{Joules}}{\text{kilograms}} = \frac{J}{kg} \]

### Step 6: Simplify the Units
Since 1 Joule is equivalent to \( 1 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \), we can rewrite the unit of gravitational potential as:
\[ V = \frac{kg \cdot m^2/s^2}{kg} = \frac{m^2}{s^2} \]

### Conclusion
Thus, the S.I. unit of gravitational potential is:
\[ \text{Joules per kilogram (J/kg)} \]

### Final Answer
The S.I. unit of gravitational potential is \( \text{J/kg} \).

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