A body is suspended from a spring balance kept in a satellite. The reading of the balance is `W_1` when the satellite goes in an orbit of radius R and is `W_2` when it goes in an orbit of radius 2R.

Options

A. `W_1=W_2`
B. `1/2mgR`
C. `mgR`
D. `W_1!=W_2`

Answer

To solve the problem, we need to understand the concept of weightlessness in a satellite orbiting the Earth.

### Step-by-Step Solution:

1. **Understanding Weight in Orbit**:
When a satellite is in orbit, both the satellite and the body inside it are in free fall. This means that they are falling towards the Earth due to gravity, but because they are also moving forward at a high speed, they keep missing the Earth. This creates a condition known as "weightlessness" for objects inside the satellite.

2. **Reading of the Spring Balance**:
The spring balance measures the weight of the body. However, since both the satellite and the body are in free fall, the body does not exert any force on the spring balance. Therefore, the reading on the spring balance will be zero.

3. **Weight Readings in Different Orbits**:
- When the satellite is in orbit of radius R, the reading of the balance is \( W_1 = 0 \).
- When the satellite is in orbit of radius 2R, the reading of the balance is \( W_2 = 0 \).

4. **Conclusion**:
Since both readings are zero, we can conclude that \( W_1 = W_2 \).

Thus, the correct answer is that \( W_1 \) is equal to \( W_2 \) and both are zero.

### Final Answer:
\( W_1 = W_2 = 0 \)