A body weight 500 N on the surface of the earth. How much would it weigh half way below the surface of the earth

Options

A. 125 N
B. 250 N
C. 500 N
D. 1000 N

Explanation

To solve the problem of how much a body weighing 500 N on the surface of the Earth would weigh halfway below the surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Weight and Gravity**:
- The weight of a body is the force exerted on it due to gravity. On the surface of the Earth, this force is given by \( W = mg \), where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.

2. **Identify the Given Values**:
- The weight of the body on the surface of the Earth is \( W = 500 \, \text{N} \).

3. **Determine the Depth**:
- We need to find the weight of the body halfway below the surface of the Earth. If \( R \) is the radius of the Earth, then halfway down would be at a depth \( D = \frac{R}{2} \).

4. **Use the Formula for Apparent Gravity**:
- The formula for the acceleration due to gravity at a depth \( D \) is given by:
\[ g' = g \left(1 - \frac{D}{R}\right) \]
- Here, \( g' \) is the apparent gravity at depth \( D \), \( g \) is the gravity at the surface, \( D \) is the depth, and \( R \) is the radius of the Earth.

5. **Substitute the Depth into the Formula**:
- Since \( D = \frac{R}{2} \):
\[ g' = g \left(1 - \frac{\frac{R}{2}}{R}\right) = g \left(1 - \frac{1}{2}\right) = g \left(\frac{1}{2}\right) \]

6. **Calculate the Apparent Weight**:
- The apparent weight \( W' \) at this depth can be calculated as:
\[ W' = mg' = m \left(g \cdot \frac{1}{2}\right) \]
- Since the weight on the surface is \( W = mg = 500 \, \text{N} \):
\[ W' = 500 \cdot \frac{1}{2} = 250 \, \text{N} \]

7. **Conclusion**:
- Therefore, the weight of the body halfway below the surface of the Earth is \( W' = 250 \, \text{N} \).

### Final Answer:
The weight of the body halfway below the surface of the Earth is **250 N**.