Intensity of gravitational field inside the hollow spherical shell is

Options

A. Variable
B. minimum
C. maximum
D. zero

Answer

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

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a hollow spherical shell with mass distributed uniformly over its surface. The shell has no mass inside it.

2. **Defining Gravitational Field**:
- The gravitational field (G) at a point in space is defined as the force experienced by a unit mass placed at that point due to the gravitational attraction of the mass distribution.

3. **Applying Gauss's Law for Gravity**:
- To find the gravitational field inside the hollow shell, we can use a concept similar to Gauss's Law in electrostatics. We consider a Gaussian surface inside the hollow shell.

4. **Analyzing the Mass Inside the Gaussian Surface**:
- Since the shell is hollow, there is no mass enclosed within the Gaussian surface that we have drawn inside the shell. Therefore, the total mass (M) inside this Gaussian surface is zero.

5. **Using Gauss's Law**:
- According to Gauss's Law for gravity, the gravitational field (G) is related to the mass enclosed by the Gaussian surface. Mathematically, it can be expressed as:
\[ G \cdot A = \frac{G \cdot M_{\text{enclosed}}}{r^2} \]
- Here, \(A\) is the area of the Gaussian surface, \(M_{\text{enclosed}}\) is the mass inside the Gaussian surface, and \(r\) is the distance from the center of the shell to the point where we are calculating the gravitational field.

6. **Conclusion**:
- Since \(M_{\text{enclosed}} = 0\), we find that:
\[ G = 0 \]
- Thus, the intensity of the gravitational field inside the hollow spherical shell is zero.

### Final Answer:
The intensity of the gravitational field inside the hollow spherical shell is **0**.

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