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, we need to analyze the two statements regarding the gravitational acceleration (g) at different points in relation to the Earth's shape and rotation.

### Step-by-Step Solution:

1. **Understanding the Bulging of the Earth**:
- The Earth is not a perfect sphere; it bulges at the equator due to its rotation. This means that the radius at the equator (r') is greater than the radius at the poles (r1).
- The average radius of the Earth (re) is between these two values, where r' > re > r1.

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

3. **Analyzing Statement A**:
- Statement A claims that there are points outside the Earth where the value of g is equal to its value at the equator.
- Since the radius at the equator (r') is greater than the average radius (re), it implies that at distances greater than r', the gravitational acceleration will decrease.
- Therefore, as we move outside the Earth, at some point where the distance from the center equals r', the value of g can indeed equal the value at the equator. Thus, **Statement A is correct**.

4. **Analyzing Statement B**:
- Statement B claims that there are points outside the Earth where the value of g is equal to its value at the poles.
- The gravitational acceleration at the poles is greater than at the equator due to the Earth's shape and rotation.
- For points outside the Earth, as we move away from the Earth, the value of g will continue to decrease. The value of g at the poles can only be matched at a point inside the Earth, not outside. Thus, **Statement B is incorrect**.

5. **Conclusion**:
- Based on the analysis, we conclude that:
- Statement A is true.
- Statement B is false.

### Final Answer:
- A is correct.
- B is incorrect.