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 analyze the situation of a body suspended from a spring balance in a satellite orbiting the Earth. We will consider two different orbits: one with radius \( R \) and the other with radius \( 2R \).

### Step-by-Step Solution:

1. **Understanding Weight in Orbit**:
- In a satellite orbiting the Earth, both the satellite and the body inside it are in free fall. This creates a condition of weightlessness for the body. The reading on the spring balance (which measures weight) will reflect this condition.

2. **Weight in the First Orbit**:
- When the satellite is at radius \( R \), the reading on the spring balance is \( W_1 \).
- Since the body is in free fall, the effective weight \( W_1 = 0 \).

3. **Weight in the Second Orbit**:
- When the satellite is at radius \( 2R \), the reading on the spring balance is \( W_2 \).
- Similarly, in this case, the body is also in free fall, so the effective weight \( W_2 = 0 \).

4. **Comparing the Two Readings**:
- Since both readings \( W_1 \) and \( W_2 \) are equal to zero due to the condition of weightlessness, we can conclude that:
\[ W_1 = W_2 \]

### Final Relation:
Thus, the relation between the two readings is:
\[ W_1 = W_2 = 0 \]