If earth is assumed to be a sphere of uniform density then plot a graph between acceleration due to gravity (g) and distance from the centre of earth.

Answer

To plot the graph between acceleration due to gravity (g) and distance from the center of the Earth, we need to understand how g varies with distance from the center.

### Step-by-Step Solution:

1. **Understanding the Concept**:
- The acceleration due to gravity (g) varies with distance from the center of the Earth. Inside the Earth, g decreases linearly with depth, while outside the Earth, g decreases with the square of the distance from the center.

2. **Inside the Earth**:
- When we are at a distance \( d \) from the center of the Earth, the effective mass that contributes to gravity is only that within a sphere of radius \( d \).
- The formula for g at a distance \( d \) from the center is given by:
\[ g(d) = g_0 \left(1 - \frac{d}{R}\right) \]
where \( g_0 \) is the acceleration due to gravity at the surface of the Earth, and \( R \) is the radius of the Earth.

3. **At the Center of the Earth**:
- At the center of the Earth (d = 0), the value of g becomes 0:
\[ g(0) = g_0 \left(1 - \frac{0}{R}\right) = 0 \]

4. **At the Surface of the Earth**:
- At the surface (d = R), g equals \( g_0 \):
\[ g(R) = g_0 \left(1 - \frac{R}{R}\right) = g_0 \]

5. **Outside the Earth**:
- For distances greater than the radius of the Earth (d > R), the acceleration due to gravity is given by:
\[ g(d) = \frac{g_0 R^2}{d^2} \]
- This indicates that g decreases with the square of the distance from the center.

6. **Plotting the Graph**:
- On the x-axis, we will plot the distance from the center of the Earth (d), ranging from 0 to a value greater than R.
- On the y-axis, we will plot the acceleration due to gravity (g).
- The graph will start at (0, 0) at the center, rise linearly to (R, g_0) at the surface, and then decrease as \( \frac{1}{d^2} \) for distances greater than R.

### Graph Description:
- The graph will have three distinct regions:
1. From the center (0) to the surface (R), g increases linearly from 0 to \( g_0 \).
2. At the surface (R), g is at its maximum \( g_0 \).
3. Beyond the surface, g decreases with the square of the distance.