Where will a body weight minimum ?

Options

A. At a height of 100 m above the earth 's surface
B. At the earth 's surface
C. At a depth of 100 m below the earth 's surface
D. At the centre of the earth

Explanation

To determine where a body's weight will be minimum among the given options, we need to analyze the effect of gravity at different positions relative to the Earth.

### Step-by-Step Solution:

1. **Understanding Weight and Gravity**:
- Weight (W) of a body is given by the formula:
\[ W = m \cdot g \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.

2. **Identifying the Options**:
- Option 1: At a height of 100 meters above the Earth's surface.
- Option 2: At the Earth's surface.
- Option 3: At a depth of 100 meters below the Earth's surface.
- Option 4: At the center of the Earth.

3. **Analyzing Each Position**:
- **At a height of 100 meters**:
- As we go above the Earth's surface, the value of \( g \) decreases. Therefore, the weight will be less than that at the surface but not zero.
- **At the Earth's surface**:
- Here, the weight is maximum because \( g \) is approximately \( 9.8 \, m/s^2 \).
- **At a depth of 100 meters**:
- As we go below the surface, the value of \( g \) also decreases. Thus, the weight will be less than that at the surface but still not zero.
- **At the center of the Earth**:
- At the center, the acceleration due to gravity \( g \) is zero. Therefore, the weight of the body will also be zero.

4. **Conclusion**:
- Comparing the weights at all four positions, the minimum weight occurs at the center of the Earth where \( g = 0 \).
- Thus, the correct answer is **Option 4: At the center of the Earth**.