The value of acceleration due to gravity at the surface of earth

Options

A. is maximum at the poles
B. is maximum at the equator
C. remains constant everywhere on the surface of the earth
D. is maximum at the international time line

Explanation

To find the value of acceleration due to gravity at the surface of the Earth and determine where it is maximum, we can follow these steps:

### Step 1: Understand the Formula for Acceleration Due to Gravity
The acceleration due to gravity (g) at the surface of the Earth can be calculated using the formula:
\[ g = \frac{GM}{R^2} \]
Where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( R \) is the radius of the Earth.

### Step 2: Analyze the Radius at Different Locations
The Earth is not a perfect sphere; it is slightly oblate. This means that the radius at the equator (\( R_e \)) is greater than the radius at the poles (\( R_p \)). Specifically, we can say:
\[ R_e > R_p \]

### Step 3: Compare the Values of g at the Poles and Equator
Since \( g \) is inversely proportional to the square of the radius (\( R^2 \)), we can conclude:
- At the poles, where the radius is the smallest (\( R_p \)), the value of \( g \) will be the largest.
- At the equator, where the radius is larger (\( R_e \)), the value of \( g \) will be smaller.

### Step 4: Conclusion
From the analysis above, we can conclude that:
- The acceleration due to gravity is maximum at the poles and minimum at the equator.
- Therefore, the correct answer to the question is that the value of acceleration due to gravity is maximum at the poles.

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

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