The gravitational potential

Options

A. is same everywhere inside a uniform spherical shell.
B. at a point is always negative.
C. is maximum at infinity.
D. of a body is the gravitational potential energy per unit mass of the body.

Answer

To solve the question regarding gravitational potential, we will analyze each of the four options provided and determine their validity based on the principles of gravitation.

### Step-by-Step Solution:

1. **Understanding Gravitational Potential**:
Gravitational potential (V) at a distance r from a mass M is given by the formula:
\[ V = -\frac{GM}{r} \]
where G is the gravitational constant.

2. **Option A: Gravitational potential is the same everywhere inside a uniform spherical shell**:
- According to the shell theorem, the gravitational field inside a uniform spherical shell is zero. Since the gravitational field is zero, the potential does not change and remains constant throughout the interior of the shell.
- **Conclusion**: This statement is **correct**.

3. **Option B: Gravitational potential at a point is always negative**:
- The gravitational potential is negative for all points outside a mass, as given by the formula. As r approaches infinity, the potential approaches zero, which is the least negative value.
- **Conclusion**: This statement is **correct**.

4. **Option C: Gravitational potential is maximum at infinity**:
- At infinity, the potential approaches zero, which is indeed the maximum value of gravitational potential (less negative than any other point).
- **Conclusion**: This statement is **correct**.

5. **Option D: Gravitational potential is the gravitational potential energy per unit mass**:
- Gravitational potential (V) is defined as the gravitational potential energy (U) per unit mass (m). Thus, \( V = \frac{U}{m} \).
- **Conclusion**: This statement is **correct**.

### Final Conclusion:
All four options (A, B, C, D) are correct regarding gravitational potential.

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