Assertion : Let `W_(1)` be the work done in taking away a satellite from the surface of earth to its orbit and then `W_(2)` the work done in rotating the satellite in circular orbit there. Then, `W_(1)=W_(2)`
Reason : `W_(2)=(GMm)/(4R)`

Options

A. If both Assertin and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is false
D. If Assertion is false but Reason is true

Explanation

To solve the problem, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the work done in moving a satellite from the surface of the Earth to its orbit (W₁) is equal to the work done in rotating the satellite in its circular orbit (W₂).

2. **Calculating W₁ (Work Done to Move the Satellite)**:
- When moving a satellite from the Earth's surface to a height \( h \), the work done can be calculated using the formula:
\[ W_1 = mgh \]
- However, since the gravitational force changes with height, we need to integrate the force over the distance. The work done against gravity when moving to a height \( h \) is:
\[ W_1 = \int_{R}^{R+h} \frac{GMm}{r^2} \, dr \]
- Evaluating this integral gives:
\[ W_1 = GMm \left( \frac{1}{R} - \frac{1}{R+h} \right) = \frac{GMm h}{R(R+h)} \]

3. **Calculating W₂ (Work Done to Rotate the Satellite)**:
- The work done to keep the satellite in circular motion at height \( h \) is related to its kinetic energy. The gravitational force provides the necessary centripetal force for circular motion.
- The speed \( v \) of the satellite in orbit is given by:
\[ v = \sqrt{\frac{GM}{R+h}} \]
- The kinetic energy (which is also the work done to maintain the satellite in orbit) is:
\[ W_2 = \frac{1}{2} mv^2 = \frac{1}{2} m \left(\frac{GM}{R+h}\right) = \frac{GMm}{2(R+h)} \]

4. **Comparing W₁ and W₂**:
- From our calculations, we have:
\[ W_1 = \frac{GMm h}{R(R+h)} \]
\[ W_2 = \frac{GMm}{2(R+h)} \]
- For \( W_1 \) to equal \( W_2 \), we would need:
\[ \frac{GMm h}{R(R+h)} = \frac{GMm}{2(R+h)} \]
- This equality does not hold true in general, indicating that the assertion \( W_1 = W_2 \) is false.

5. **Evaluating the Reason**:
- The reason states that \( W_2 = \frac{GMm}{4R} \). This is incorrect based on our calculation of \( W_2 \), which is \( \frac{GMm}{2(R+h)} \).

### Conclusion:
- The assertion is false, and the reason is also false. Therefore, the statement "if assertion is false but reason is true" is incorrect.