The weight of a body on the earth is `400 N`.Then weight of the body when taken to a depht half of the radius of the earth will be :

Options

A. `Zero`
B. `200 N`
C. `100 N`
D. `300 N`

Answer

To solve the problem of finding the weight of a body when taken to a depth that is half of the radius of the Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- The weight of the body on the surface of the Earth is given as \( W = 400 \, \text{N} \).
- We need to find the weight of the body at a depth \( h = \frac{R}{2} \), where \( R \) is the radius of the Earth.

2. **Using the Formula for Weight at Depth**:
- The formula for gravitational acceleration \( g' \) at a depth \( h \) is given by:
\[ g' = g \left(1 - \frac{h}{R}\right) \]
- Here, \( g \) is the acceleration due to gravity at the surface of the Earth.

3. **Substituting the Depth**:
- Since \( h = \frac{R}{2} \), we substitute this into the formula:
\[ g' = g \left(1 - \frac{\frac{R}{2}}{R}\right) \]
- Simplifying this gives:
\[ g' = g \left(1 - \frac{1}{2}\right) = g \left(\frac{1}{2}\right) \]
- Thus, \( g' = \frac{g}{2} \).

4. **Relating Weight at Depth to Weight on Surface**:
- The weight of the body at depth can be expressed as:
\[ W' = m g' \]
- Substituting \( g' \) from the previous step:
\[ W' = m \left(\frac{g}{2}\right) \]
- Since the weight at the surface is \( W = mg \), we can write:
\[ W' = \frac{1}{2} W \]

5. **Calculating the Weight at Depth**:
- Given \( W = 400 \, \text{N} \):
\[ W' = \frac{1}{2} \times 400 \, \text{N} = 200 \, \text{N} \]

### Final Answer:
The weight of the body when taken to a depth half of the radius of the Earth is \( W' = 200 \, \text{N} \).