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 problem of how the acceleration due to gravity (g) varies from the center of the Earth to its surface, we can follow these steps:

### Step 1: Understanding the formula for gravity inside the Earth
The acceleration due to gravity at a depth \( d \) below the surface of the Earth is given by the formula:
\[ g_{\text{depth}} = g_{\text{surface}} \left(1 - \frac{d}{R}\right) \]
where:
- \( g_{\text{depth}} \) is the acceleration due to gravity at depth \( d \),
- \( g_{\text{surface}} \) is the acceleration due to gravity at the surface of the Earth,
- \( R \) is the radius of the Earth.

### Step 2: Analyzing the formula
From the formula, we can see that as \( d \) increases (moving deeper into the Earth), the term \( \frac{d}{R} \) increases, which means \( g_{\text{depth}} \) decreases linearly. At the center of the Earth (where \( d = R \)), \( g_{\text{depth}} \) becomes zero.

### Step 3: Behavior of gravity above the Earth's surface
For heights above the Earth's surface, the formula for gravity is:
\[ g_{\text{height}} = g_{\text{surface}} \frac{R^2}{(R + h)^2} \]
where \( h \) is the height above the surface. As \( h \) increases, \( g_{\text{height}} \) decreases.

### Step 4: Graphical representation
1. From the center of the Earth to the surface (depth \( d \)), \( g \) starts from 0 and increases linearly to \( g_{\text{surface}} \).
2. From the surface to a height \( h \), \( g \) decreases as \( h \) increases.

### Conclusion
The variation of \( g \) can be visualized as a linear increase from 0 at the center to \( g_{\text{surface}} \) at the surface, followed by a decrease as we move above the surface. Therefore, the correct graph representing this variation is option B.