Take the effect of bulging of earth and its rotation in account. Consider the following statements:
A. There are pints outside the earth where the earth of g is equal to its value at the equator.
B.There are points outside the earth where the earth where the value of g is equla to its value at the poles.

Options

A. both A and B are true
B. A is true but B is false
C. B is true but A is false
D. both and B are false

Answer

To solve the problem regarding the effects of the Earth's bulging and rotation on the gravitational acceleration \( g \), we will analyze the two statements provided:

**Statement A:** There are points outside the Earth where the value of \( g \) is equal to its value at the equator.

**Statement B:** There are points outside the Earth where the value of \( g \) is equal to its value at the poles.

### Step-by-Step Solution:

1. **Understanding Gravitational Acceleration \( g \):**
The gravitational acceleration \( g \) at a distance \( R \) from the center of the Earth is given by the formula:
\[ g = \frac{G M}{R^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( R \) is the distance from the center of the Earth.

2. **Effect of Earth's Shape:**
The Earth is not a perfect sphere; it is an oblate spheroid due to its rotation. This means that the radius at the equator is greater than the radius at the poles. Therefore, the value of \( g \) is different at the equator and the poles:
- At the equator, \( g \) is slightly less due to the centrifugal force caused by Earth's rotation.
- At the poles, \( g \) is slightly greater because there is no centrifugal force acting on objects.

3. **Analyzing Statement A:**
- Since the equatorial radius is larger, the gravitational force decreases with distance from the center of the Earth.
- There are points outside the Earth where the gravitational acceleration \( g \) can equal its value at the equator. This can occur at a specific distance from the center of the Earth where the gravitational pull equals that at the equator. Therefore, **Statement A is correct.**

4. **Analyzing Statement B:**
- The gravitational acceleration at the poles is greater than at the equator. For points outside the Earth, the gravitational force decreases with distance.
- To find points where \( g \) equals that at the poles, we would need to consider points inside the Earth, as the gravitational pull decreases with increasing distance from the center. Thus, **Statement B is incorrect.**

### Conclusion:
- **Statement A is correct.**
- **Statement B is incorrect.**