The period of moon's rotation around the earth is approx. 29 days. IF moon's mass were 2 fold its present value and all other things remain unchanged, the period of Moon's rotation would be nearly

Options

A. `29sqrt(2)` days
B. `(29)/(sqrt(2))` days
C. `29xx2` days
D. 29 days

Explanation

To solve the problem, we need to analyze how the period of the Moon's rotation around the Earth is affected by changes in the Moon's mass.

### Step-by-Step Solution:

1. **Understand the Formula for the Period of Rotation**:
The period \( T \) of an object in circular motion is given by the formula:
\[ T = 2\pi \sqrt{\frac{r^3}{GM}} \]
where:
- \( r \) is the distance from the center of the Earth to the Moon,
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth.

2. **Identify the Parameters**:
In this scenario, we are given that the Moon's mass is doubled. However, the formula shows that the period \( T \) does not depend on the mass of the satellite (the Moon in this case) but rather on the mass of the Earth and the distance \( r \).

3. **Analyze the Effect of Doubling the Moon's Mass**:
Since the period \( T \) is independent of the mass of the Moon, doubling the Moon's mass will not affect the period of its rotation around the Earth. Therefore, the period remains the same.

4. **Conclusion**:
The period of the Moon's rotation around the Earth will still be approximately 29 days, regardless of the change in the Moon's mass.

### Final Answer:
The period of the Moon's rotation would be nearly **29 days**.