Question

Inside a uniform spherical shell :
(a) the gravitational field is zero.
(b) the gravitational potential is zero.
(c) the gravitational field is same everywhere.
(d) the gravitation potential is same everywhere.
(e) all of the above
Choose the most appropriate answer from the options given below :

• A. (b), (c) and (d) only
• B. (a), (b) and (c) only
• C. (a), (c) and (d) only
• D. (e) only

Hint:

While the gravitational field (force per unit mass) is zero inside a shell, the potential is a constant negative value equal to the potential at the surface.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The shell theorem in gravitation states that the gravitational influence inside a uniform spherical shell follows specific rules based on the inverse square law.
Step 2: Detailed Explanation:
1. Statement (a) and (c): The gravitational field (\(g\)) inside a uniform shell is zero at all points. Since zero is the same value at every point, it is correct to say the field is zero and that it is the same everywhere.
2. Statement (b) and (d): The gravitational potential (\(V\)) inside the shell is given by \(V = -GM/R\), where \(R\) is the shell radius. This is a constant value but is NOT zero. Since it is constant, it is the same everywhere inside the shell.
Conclusion: (a), (c), and (d) are true. (b) is false.
Step 3: Final Answer:
The correct option is (C), which includes (a), (c), and (d).