In some region, the gravitational field is zero. The gravitational potential in this region

Options

A. must be variable
B. must be constant
C. can not be zero
D. must be zero

Answer

To solve the question, we need to analyze the relationship between gravitational field and gravitational potential.

### Step-by-Step Solution:

1. **Understanding Gravitational Field and Potential**:
The gravitational field (E) is related to the gravitational potential (V) by the equation:
\[ E = -\frac{dV}{dr} \]
where \( \frac{dV}{dr} \) is the gradient (or derivative) of the gravitational potential with respect to distance.

2. **Given Condition**:
The problem states that in a certain region, the gravitational field is zero:
\[ E = 0 \]

3. **Implication of Zero Gravitational Field**:
If the gravitational field is zero, substituting into the equation gives:
\[ 0 = -\frac{dV}{dr} \]
This implies that:
\[ \frac{dV}{dr} = 0 \]

4. **Conclusion about Gravitational Potential**:
The condition \( \frac{dV}{dr} = 0 \) means that the gravitational potential \( V \) does not change with respect to distance \( r \). Therefore, the gravitational potential must be constant in that region.

5. **Constant Value of Gravitational Potential**:
The constant value of gravitational potential can either be zero or some non-zero value. However, the key point is that it does not vary; it remains constant.

6. **Final Answer**:
Thus, we conclude that the gravitational potential in the region where the gravitational field is zero must be constant.

### Answer:
The gravitational potential in this region must be constant.