If the mass of a revolving around the sun is doubled and its frequency of revolution remains constant then the radius of its orbit will be

Options

A. Doubled
B. Thnce
C. Halved
D. Remain same

Answer

To solve the problem, we need to analyze the relationship between the mass of an object revolving around the sun, its frequency of revolution, and the radius of its orbit.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- The mass of the object (let's denote it as \( m \)) is doubled, so it becomes \( 2m \).
- The frequency of revolution remains constant. This means the time period \( T \) of revolution also remains constant since frequency \( f \) is inversely related to time period \( T \) (i.e., \( f = \frac{1}{T} \)).

2. **Using Kepler's Third Law**:
- According to Kepler's Third Law, the square of the time period \( T \) of a planet's orbit is directly proportional to the cube of the semi-major axis (radius \( r \) for circular orbits) of its orbit:
\[ T^2 \propto r^3 \]
- This can also be expressed as:
\[ T^2 = \frac{4\pi^2}{GM} r^3 \]
where \( G \) is the gravitational constant and \( M \) is the mass of the sun.

3. **Analyzing the Effect of Doubling Mass**:
- In the formula \( T^2 = \frac{4\pi^2}{GM} r^3 \), the mass \( m \) of the revolving object does not appear. Only the mass of the sun \( M \) is present.
- Since the mass of the revolving object is doubled, it does not affect the radius \( r \) or the time period \( T \) because the equation is independent of the mass of the object in orbit.

4. **Conclusion**:
- Since the frequency (and thus the time period) remains constant, and the mass of the object does not affect the radius in the equation, the radius of the orbit will remain unchanged.

### Final Answer:
The radius of its orbit will remain the same.