Assertion: If there are no external forces, the center of mass of a double star moves like a free particle.
Reason: If we go to the center of mass frame, then we find that the two stars are moving in a circle about the center of mass, which is at rest.

Options

A. Both assertion and reason are true and reason is the correct explanation of assertion.
B. Both assertion and reason are true but reason is not the correct explanation of assertion
C. Assertion is true but reason is false.
D. Both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided, and determine their validity.

### Step 1: Understand the Assertion
The assertion states that if there are no external forces acting on a double star system, the center of mass of the system moves like a free particle.

- In a double star system (or binary star system), two stars orbit around a common center of mass. If there are no external forces acting on the system, the center of mass will maintain its position and move uniformly, similar to how a free particle would move.

### Step 2: Understand the Reason
The reason states that if we go to the center of mass frame, we find that the two stars are moving in a circle about the center of mass, which is at rest.

- In the center of mass frame, the center of mass is stationary. The two stars will indeed orbit around this point. This circular motion is a result of the gravitational attraction between the two stars, and since the distance between them remains constant, their motion is stable.

### Step 3: Analyze the Relationship Between Assertion and Reason
- Both the assertion and the reason are true:
- The assertion is true because the center of mass does behave like a free particle when no external forces are acting on it.
- The reason is also true because in the center of mass frame, the stars do move in a circular path around the center of mass.

### Step 4: Determine if the Reason is the Correct Explanation of the Assertion
- While both statements are true, the reason does not adequately explain why the assertion is true. The assertion is based on the absence of external forces, while the reason focuses on the motion of the stars in the center of mass frame.

### Conclusion
Thus, the correct answer is that both the assertion and reason are true, but the reason is not the correct explanation for the assertion. Therefore, the answer is option B.