At the centre of earth the acceleration due to gravity is

Options

A. infinite
B. zero
C. `9.8 ms^(-2)`
D. all of these

Explanation

To solve the question "At the center of the Earth, the acceleration due to gravity is:", we can follow these steps:

### Step 1: Understand the Concept of Acceleration Due to Gravity
The acceleration due to gravity (g) is the acceleration experienced by an object due to the gravitational force exerted by a massive body, such as the Earth. On the surface of the Earth, this value is approximately 9.8 m/s².

### Step 2: Recall the Formula for Acceleration Due to Gravity
The formula for calculating the acceleration due to gravity at a distance from the center of a planet is given by:
\[ g = \frac{GM}{r^2} \]
Where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the planet,
- \( r \) is the distance from the center of the planet.

### Step 3: Analyze the Situation at the Center of the Earth
At the center of the Earth:
- The distance \( r \) from the center to itself is 0.
- The mass \( M \) that exerts gravitational force at the center is effectively 0, because we are considering the gravitational pull from all the surrounding mass, which cancels out at the center.

### Step 4: Substitute Values into the Formula
Substituting \( M = 0 \) and \( r = 0 \) into the formula:
\[ g = \frac{G \cdot 0}{0^2} \]
This expression is undefined because we cannot divide by zero, but conceptually, since there is no mass at the center, we conclude that the gravitational force is effectively zero.

### Step 5: Conclusion
Therefore, the acceleration due to gravity at the center of the Earth is:
\[ g = 0 \, \text{m/s}^2 \]

### Final Answer
The acceleration due to gravity at the center of the Earth is **0**.

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