Inside a uniform spherical shell

Options

A. the gravitational potential si zero
B. the gravitational field is zero
C. the gravitational potential is same everywhere
D. the gravitational field is same everywhere

Answer

To solve the question regarding the gravitational properties inside a uniform spherical shell, we will analyze the gravitational potential and gravitational field within the shell step by step.

### Step-by-Step Solution:

1. **Understanding the Concept of Gravitational Field and Potential:**
- The gravitational field (E) at a point is defined as the force experienced by a unit mass placed at that point.
- The gravitational potential (V) at a point is defined as the work done in bringing a unit mass from infinity to that point.

2. **Gravitational Field Inside a Uniform Spherical Shell:**
- According to the shell theorem, the gravitational field inside a uniform spherical shell is zero. This means that if you are inside the shell, you will not experience any gravitational force due to the mass of the shell surrounding you.

3. **Gravitational Potential Inside a Uniform Spherical Shell:**
- The gravitational potential inside the shell is constant and is equal to the potential at the surface of the shell. However, it is not zero. The potential is the same at all points inside the shell.

4. **Analyzing the Options:**
- **Option A:** "The gravitational potential is zero." - This is incorrect because the gravitational potential inside the shell is not zero; it is constant and equal to the potential at the surface.
- **Option B:** "The gravitational field is zero." - This is correct, as established by the shell theorem.
- **Option C:** "The gravitational potential is the same everywhere." - This is also correct, as the potential is constant throughout the interior of the shell.
- **Option D:** "The gravitational field is the same everywhere." - This is misleading because while the gravitational field is zero everywhere inside the shell, it does not imply that it is "the same" in a non-zero sense; however, it is technically correct in the context of being zero everywhere.

5. **Conclusion:**
- The correct statements are B, C, and D. Therefore, the answer to the question is that options B, C, and D are true.

### Final Answer:
The correct options are B, C, and D.