What is the intensity of gravitational field of the centre of a spherical shell

Options

A. `Gm//r^(2)`
B. `g`
C. Zero
D. None of these

Answer

To find the intensity of the gravitational field at the center of a spherical shell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Gravitational Field**: The gravitational field intensity (E) at a point in space is defined as the force (F) experienced by a unit mass (m) placed at that point. Mathematically, it is given by:
\[ E = \frac{F}{m} \]

2. **Properties of a Spherical Shell**: A spherical shell is a hollow object with mass distributed uniformly over its surface. According to the shell theorem, the gravitational field inside a hollow spherical shell is zero at any point within the shell.

3. **Analyzing the Center of the Shell**: At the center of the spherical shell, the symmetry of the mass distribution means that the gravitational forces exerted by different parts of the shell cancel each other out. Each mass element on the shell pulls on a mass located at the center, but due to symmetry, these forces balance out.

4. **Conclusion about Gravitational Field Intensity**: Since the net gravitational force acting on a mass placed at the center of the spherical shell is zero, the intensity of the gravitational field (E) at the center is:
\[ E = 0 \, \text{N/kg} \]

### Final Answer:
The intensity of the gravitational field at the center of a spherical shell is **0 N/kg**.

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