The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity.

Options

A. will be directed towards the centre but not the same everywhere
B. will have the same value everywhere but not directed towards the centre
C. will be same everywhere in magnitude directed towards the same
D. cannot be zero at any point

Explanation

To solve the problem regarding the acceleration due to gravity on the surface of the Earth when the interior has a non-uniform density, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Gravity**:
The acceleration due to gravity \( g \) at the surface of the Earth is influenced by the mass of the Earth and the distance from its center. The formula for gravitational acceleration is given by:
\[ g = \frac{GM}{r^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the radius of the Earth.

2. **Assumption of Uniform Density**:
Initially, we assume that the Earth has a uniform density. Under this assumption, the gravitational force is the same at all points on the surface of the Earth.

3. **Considering Non-Uniform Density**:
When the density of the Earth is not uniform, different regions of the Earth will exert different gravitational forces at the surface. For example, if we consider two points on the surface, \( G_1 \) and \( G_2 \), where the density of the Earth below \( G_1 \) is higher than that below \( G_2 \), the gravitational acceleration will differ.

4. **Analyzing the Effect of Density**:
- The gravitational force at point \( G_1 \) will be greater than at point \( G_2 \) because:
- The mass of the Earth beneath \( G_1 \) is greater due to higher density.
- The distance from the center is the same for both points, but the effective mass contributing to gravity at \( G_1 \) is larger.

5. **Conclusion on the Variation of Gravity**:
Since the gravitational acceleration \( g \) depends on the mass and the distance, in regions of non-uniform density, the value of \( g \) will not be the same everywhere. It will vary based on the density distribution within the Earth.

6. **Direction of Gravity**:
The direction of the gravitational force will always be towards the center of the Earth. However, due to the varying density, the resultant gravitational force may not be uniform in magnitude across the surface.

7. **Final Statement**:
Thus, the acceleration due to gravity on the surface of the Earth will not be the same everywhere when the interior has non-uniform density. It will vary depending on the local density of the Earth beneath the surface.