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 determine the variation of acceleration due to gravity (g) starting from the center of the Earth to the surface, we can follow these steps:

### Step 1: Understand the formula for g inside the Earth
When we are at a depth \(d\) inside the Earth, the acceleration due to gravity \(g'\) can be expressed as:
\[ g' = g \left(1 - \frac{d}{R}\right) \]
where:
- \(g\) is the acceleration due to gravity at the surface of the Earth,
- \(d\) is the depth below the surface,
- \(R\) is the radius of the Earth.

### Step 2: Analyze the relationship
From the formula, we can see that as the depth \(d\) increases (moving from the surface to the center of the Earth), the value of \(g'\) decreases linearly. This means that at the center of the Earth (where \(d = R\)), \(g' = 0\).

### Step 3: Plot the variation of g
- At the surface (depth \(d = 0\)), \(g' = g\).
- As we move towards the center (increasing \(d\)), \(g'\) decreases linearly until it reaches \(0\) at the center (depth \(d = R\)).
- The graph of \(g'\) versus \(d\) will be a straight line starting from \(g\) at \(d = 0\) and reaching \(0\) at \(d = R\).

### Step 4: Identify the correct option
Given the linear decrease of \(g'\) with increasing depth, we can conclude that the correct representation of this variation is a straight line that slopes downwards from \(g\) to \(0\).

### Conclusion
Thus, the variation of \(g\) starting from the center of the Earth to the surface is represented by a linear graph that decreases from \(g\) to \(0\).