In a gravitational field, at a point where the gravitational potential is zero

Options

A. The gravitational field is necessarily zero
B. The gravitational field is not necessarily zero
C. Nothing can be said definitely about the gravitational field
D. None of these

Answer

To solve the question regarding the gravitational field at a point where the gravitational potential is zero, we can follow these steps:

### Step 1: Understand the relationship between gravitational potential and gravitational field
The gravitational potential (V) at a point in a gravitational field is related to the gravitational field (E) by the equation:
\[ E = -\frac{dV}{dr} \]
This means that the gravitational field is the negative gradient of the gravitational potential.

### Step 2: Analyze the condition of zero gravitational potential
If the gravitational potential (V) is zero at a certain point, we need to consider what this implies about the gravitational field (E) at that point.

### Step 3: Evaluate the implications of zero potential
If V = 0 at a point, it does not necessarily mean that the gravitational field (E) is also zero. The gravitational field can still have a non-zero value while the potential is zero. For example, the potential can be zero at a point in space where the gravitational field is directed towards a mass.

### Step 4: Consider the definition of gravitational potential
Gravitational potential is defined as the work done per unit mass to bring a mass from infinity to that point. Therefore, if we are at a point where the potential is zero, it means that the work done to bring a mass from infinity to that point is zero, but it does not imply that the gravitational field itself is zero.

### Step 5: Conclusion
Thus, the statement that "where the gravitational potential is zero, the gravitational field will also be zero" is incorrect. The gravitational field can exist even when the potential is zero.

### Final Answer
The gravitational field does not have to be zero at a point where the gravitational potential is zero.

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