Which of the following statements is/are correct?
If we dug a tunnel through the body of the earth and put an object into it, its will undergo simple harmonic motion, oscillating in to between two extreme surfaces of the earth
The value of g is zero at the centre of the earth.Choose the correct option.

Options

A. Only I
B. I and II
C. Only II
D. None of these

Answer

To solve the question, we need to analyze the two statements provided and determine their correctness based on the principles of gravitation and simple harmonic motion.

### Step-by-Step Solution:

1. **Understanding Statement 1**:
- The statement claims that if we dug a tunnel through the Earth and placed an object into it, the object would undergo simple harmonic motion (SHM) oscillating between the two extreme surfaces of the Earth.
- When an object is dropped into a tunnel that goes through the center of the Earth, it experiences a gravitational force that varies with depth. The force acting on the object can be derived from the gravitational attraction of the mass of the Earth that is at a radius less than the distance from the center.
- The acceleration of the object at a depth \(d\) is given by \(g' = g \left(1 - \frac{d}{R}\right)\), where \(g\) is the acceleration due to gravity at the surface and \(R\) is the radius of the Earth.
- As the object moves towards the center, the force decreases linearly, and at the center, the gravitational force becomes zero. This results in the object oscillating back and forth, exhibiting simple harmonic motion.

2. **Understanding Statement 2**:
- The second statement asserts that the value of \(g\) (acceleration due to gravity) is zero at the center of the Earth.
- At the center of the Earth, the gravitational pull from all sides cancels out, resulting in no net gravitational force acting on an object. Therefore, the value of \(g\) indeed becomes zero at the center.

3. **Conclusion**:
- Both statements are correct. Statement 1 correctly describes the behavior of an object in a tunnel through the Earth as undergoing simple harmonic motion, and Statement 2 correctly states that the value of \(g\) is zero at the center of the Earth.

4. **Final Answer**:
- The correct option is that both statements are correct.