Compare the weigths of a body when it is kept (i) 400m above the surface of the earth and (ii) 800 m below the surface of the earth.

Explanation

To compare the weights of a body when it is (i) 400 m above the surface of the Earth and (ii) 800 m below the surface of the Earth, we will use the formulas for gravitational acceleration at different heights and depths.

### Step-by-Step Solution:

1. **Understand the Problem:**
We need to find the weight of a body at two different positions: 400 m above the Earth's surface and 800 m below the Earth's surface. The weight of a body is given by the formula:
\[ W = m \cdot g \]
where \( W \) is the weight, \( m \) is the mass of the body, and \( g \) is the acceleration due to gravity.

2. **Weight Above the Surface:**
For a height \( h \) above the Earth's surface, the formula for \( g \) is:
\[ g_h = g \left(1 - \frac{2h}{R}\right) \]
where \( g \) is the acceleration due to gravity at the surface of the Earth and \( R \) is the radius of the Earth. For \( h = 400 \) m:
\[ g_{400} = g \left(1 - \frac{2 \times 400}{R}\right) \]

3. **Weight Below the Surface:**
For a depth \( d \) below the Earth's surface, the formula for \( g \) is:
\[ g_d = g \left(1 - \frac{d}{R}\right) \]
For \( d = 800 \) m:
\[ g_{800} = g \left(1 - \frac{800}{R}\right) \]

4. **Calculate the Weights:**
Now we can express the weights at both positions:
- Weight at 400 m above the surface:
\[ W_{above} = m \cdot g_{400} = m \cdot g \left(1 - \frac{2 \times 400}{R}\right) \]
- Weight at 800 m below the surface:
\[ W_{below} = m \cdot g_{800} = m \cdot g \left(1 - \frac{800}{R}\right) \]

5. **Compare the Weights:**
To compare the weights, we can take the ratio:
\[ \frac{W_{above}}{W_{below}} = \frac{g \left(1 - \frac{2 \times 400}{R}\right)}{g \left(1 - \frac{800}{R}\right)} = \frac{1 - \frac{800}{R}}{1 - \frac{800}{R}} \]
Since \( g \) cancels out, we can simplify this to:
\[ W_{above} = W_{below} \]

6. **Conclusion:**
Therefore, the weight of the body at 400 m above the surface of the Earth is equal to the weight of the body at 800 m below the surface of the Earth.

### Final Answer:
The weight of the body at 400 m above the Earth's surface is equal to the weight of the body at 800 m below the Earth's surface.