The graph that represents variation of g with depth (d) from the surface of the earth is

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Explanation

To determine the graph that represents the variation of gravitational acceleration \( g \) with depth \( d \) from the surface of the Earth, we can follow these steps:

### Step 1: Understand the relationship between \( g \) and depth \( d \)

The acceleration due to gravity \( g \) at a depth \( d \) inside the Earth can be expressed using the formula:

\[ g' = g - \frac{g d}{R} \]

where:
- \( g' \) is the acceleration due to gravity at depth \( d \),
- \( g \) is the acceleration due to gravity at the surface of the Earth,
- \( R \) is the radius of the Earth.

### Step 2: Analyze the formula

From the formula, we can see that as \( d \) increases (i.e., as we go deeper into the Earth), the term \( \frac{g d}{R} \) increases. This means that \( g' \) decreases as \( d \) increases.

### Step 3: Determine the behavior of \( g' \)

- At \( d = 0 \) (the surface), \( g' = g \).
- As \( d \) increases towards the center of the Earth, \( g' \) decreases linearly because the term \( \frac{g d}{R} \) increases linearly with \( d \).

### Step 4: Sketch the graph

The graph of \( g' \) versus \( d \) will start at \( g \) when \( d = 0 \) and will decrease linearly as \( d \) increases. Therefore, the graph will be a straight line that slopes downwards.

### Step 5: Conclusion

The correct representation of the variation of \( g \) with depth \( d \) is a straight line that starts from \( g \) at \( d = 0 \) and decreases linearly as \( d \) increases.