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

Explanation

To solve the problem of how the period of the Moon's rotation around the Earth changes if the Moon's mass is doubled, we can follow these steps:

### Step 1: Understand the formula for the period of rotation
The period \( T \) of an object in circular motion is given by the formula:
\[ T = \frac{2\pi r}{v} \]
where \( r \) is the radius of the orbit and \( v \) is the orbital velocity.

### Step 2: Determine the orbital velocity
The orbital velocity \( v \) can be derived from the gravitational force and centripetal force balance. The formula for orbital velocity is:
\[ v = \sqrt{\frac{GM}{r}} \]
where \( G \) is the gravitational constant and \( M \) is the mass of the Earth.

### Step 3: Substitute the velocity into the period formula
Substituting the expression for \( v \) into the period formula gives:
\[ T = \frac{2\pi r}{\sqrt{\frac{GM}{r}}} \]
This simplifies to:
\[ T = 2\pi \sqrt{\frac{r^3}{GM}} \]

### Step 4: Analyze the dependence of the period on mass
From the final formula \( T = 2\pi \sqrt{\frac{r^3}{GM}} \), we can see that the period \( T \) depends on the radius \( r \) and the mass of the Earth \( M \), but **not** on the mass of the Moon. This means that changing the mass of the Moon does not affect the period of its rotation around the Earth.

### Step 5: Conclusion
Since the mass of the Moon is doubled but all other factors remain unchanged, the period of the Moon's rotation will still be:
\[ T \approx 29 \text{ days} \]

Thus, the final answer is that the period of the Moon's rotation would remain approximately 29 days.

---