Acceleration due to gravity is maximum at

Options

A. The centre of earth
B. At 100 km above the earth's surface
C. The surface of the earth
D. Infinity

Answer

To determine where the acceleration due to gravity is maximum, we can analyze the behavior of gravitational acceleration at different locations relative to the Earth.

### Step-by-Step Solution:

1. **Understanding the Concept of Gravitational Acceleration**:
- The acceleration due to gravity (g) varies depending on the distance from the center of the Earth. It is affected by both height above the Earth's surface and depth below the surface.

2. **Formula for Gravitational Acceleration at Height**:
- The formula for gravitational acceleration at a height \( h \) above the Earth's surface is given by:
\[ g_h = \frac{g}{(1 + \frac{h}{R})^2} \]
- Here, \( g \) is the acceleration due to gravity at the surface, and \( R \) is the radius of the Earth. As \( h \) increases, \( g_h \) decreases.

3. **Formula for Gravitational Acceleration at Depth**:
- The formula for gravitational acceleration at a depth \( d \) below the Earth's surface is:
\[ g_d = g \left(1 - \frac{d}{R}\right) \]
- As \( d \) increases (moving towards the center), \( g_d \) decreases as well.

4. **Analyzing the Options**:
- **At the center of the Earth**: The gravitational acceleration is zero because all the mass of the Earth is distributed around you.
- **At 100 km above the Earth's surface**: The gravitational acceleration is less than that at the surface due to the height.
- **At the surface of the Earth**: This is where the gravitational acceleration is maximum.
- **At infinity**: The gravitational acceleration approaches zero as you move infinitely far away from the Earth.

5. **Conclusion**:
- From the analysis, the maximum value of gravitational acceleration occurs at the surface of the Earth. Therefore, the correct answer is:
- **The surface of the Earth**.

### Final Answer:
The acceleration due to gravity is maximum at the **surface of the Earth**.

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