Let `V_(G)` and `E_(G)` denote gravitational potential and field respectively, then choose the wrong statement.

Options

A. `V_(G)=0, E_(g)=0`
B. `V_(G)!=0,E_(G)=0`
C. `V_(G)=0,E_(G)!=0`
D. `V_(G)!=0,E_(G)!=0`

Answer

To solve the question, we need to analyze the statements regarding gravitational potential \( V_G \) and gravitational field \( E_G \) to identify the incorrect one.

### Step-by-Step Solution:

1. **Understanding Gravitational Potential \( V_G \)**:
- Gravitational potential \( V_G \) at a point in a gravitational field is defined as the work done per unit mass in bringing a small mass from infinity to that point against the gravitational force.
- Mathematically, it can be expressed as:
\[ V_G = -\int \vec{E_G} \cdot d\vec{r} \]
- Here, \( \vec{E_G} \) is the gravitational field vector.

2. **Understanding Gravitational Field \( E_G \)**:
- The gravitational field \( E_G \) at a point is defined as the force experienced by a unit mass placed at that point.
- It can be expressed as:
\[ E_G = -\frac{dV_G}{dr} \]

3. **Analyzing the Statements**:
- We need to evaluate the statements given in the question. Typically, the statements will involve relationships between \( V_G \) and \( E_G \) under various conditions.
- For example, if \( E_G = 0 \), it implies that there is no gravitational force acting at that point, which would also imply that the potential \( V_G \) is constant (not necessarily zero).

4. **Identifying the Wrong Statement**:
- A common misconception is that if \( E_G = 0 \), then \( V_G \) must also be zero. This is incorrect. \( V_G \) can be a constant value (not necessarily zero) when \( E_G = 0 \).
- Therefore, if one of the statements claims that \( V_G \) must be zero when \( E_G = 0 \), that statement is the wrong one.

5. **Conclusion**:
- After analyzing the relationships and definitions, we conclude that the statement claiming \( V_G = 0 \) when \( E_G = 0 \) is incorrect.

### Final Answer:
The wrong statement is the one that claims \( V_G = 0 \) when \( E_G = 0 \).