Starting from the centre of the earth having radius R the variation of g (acceleration due to gravity) is shown by

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the variation of acceleration due to gravity (g) starting from the center of the Earth with radius R, we will derive the relationship and analyze the options provided.

### Step-by-Step Solution:

1. **Understanding the Concept**:
- The acceleration due to gravity (g) varies with depth inside the Earth. At the surface of the Earth, g is maximum, and it decreases as we go deeper.

2. **Formula for g at Depth**:
- The formula for the acceleration due to gravity at a depth \( d \) inside the Earth is given by:
\[ g' = g \left(1 - \frac{d}{R}\right) \]
- Here, \( g' \) is the acceleration due to gravity at depth \( d \), \( g \) is the acceleration due to gravity at the surface, \( R \) is the radius of the Earth, and \( d \) is the depth below the surface.

3. **Analyzing the Formula**:
- From the formula, we can see that as \( d \) increases (i.e., as we go deeper), \( g' \) decreases linearly. This indicates a linear relationship between \( g' \) and \( d \).

4. **Graphical Representation**:
- If we plot \( g' \) against \( d \), the graph will be a straight line starting from \( g \) at \( d = 0 \) (surface) and decreasing to \( 0 \) at \( d = R \) (center of the Earth).

5. **Conclusion**:
- Therefore, the variation of \( g \) as we move from the center of the Earth to the surface is linear and decreases from \( g \) to \( 0 \). This means that the correct option must represent a linear decrease of \( g \) with increasing depth.

### Final Answer:
The correct option is the one that shows a linear decrease in \( g \) as we move from the surface to the center of the Earth.