The variation of g with height or depth (r ) is shown correctly by the graph in Fig .4.2 (where R is radius of the earth),

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Answer

To analyze the variation of gravitational acceleration (g) with height and depth, we can break down the problem into several steps:

### Step 1: Understanding the Regions
1. **Above the Surface of the Earth**: When we are at a height above the Earth's surface, the distance from the center of the Earth (r) is greater than the Earth's radius (R).
- Here, \( g \) decreases as \( r \) increases.
- The formula for gravitational acceleration at height \( h \) above the surface is given by:
\[ g = \frac{GM}{r^2} \]
- Since \( r = R + h \), as \( h \) increases, \( g \) decreases.

### Step 2: At the Surface of the Earth
2. **On the Surface of the Earth**: At the surface, \( r = R \).
- The gravitational acceleration is maximum and is given by:
\[ g = \frac{GM}{R^2} \]
- This is the point where \( g \) has its highest value, approximately \( 9.8 \, \text{m/s}^2 \).

### Step 3: Inside the Earth
3. **Below the Surface of the Earth**: When we are at a depth \( d \) inside the Earth, the distance from the center of the Earth (r) is less than the Earth's radius (R).
- The formula for gravitational acceleration at a depth \( d \) is:
\[ g = \frac{GM}{R^3} \cdot r \]
- Here, \( r \) is the distance from the center of the Earth, which decreases as we go deeper. Thus, \( g \) decreases linearly with depth until it reaches zero at the center of the Earth.

### Step 4: Graphing the Variation
4. **Graphing**:
- On the graph, the x-axis represents the distance from the center of the Earth (r), while the y-axis represents the gravitational acceleration (g).
- **For \( r < R \)** (inside the Earth): The graph is a straight line increasing from (0,0) to (R, g_max).
- **At \( r = R \)** (on the surface): The graph reaches its maximum value \( g = \frac{GM}{R^2} \).
- **For \( r > R \)** (above the surface): The graph curves downward, showing that \( g \) decreases as \( r \) increases.

### Conclusion
From the analysis, we can conclude that:
- As we move from the center of the Earth to the surface, \( g \) increases.
- At the surface, \( g \) is maximum.
- As we move above the surface, \( g \) decreases.