Two astronauts A and B connected with a rope stay stationary in free space relative to their spaceship. Mass of A is more than that of B and the rope is straight. Astronaut A statas pulling the rope but astronaut B does not. If you were the third astronaut in the spaceship, what do you observe?

Options

A. Astronaut B accelerates towards A and A remains stateionery.
B. Both accelerate towards each other with equal accelerations of equal modulus.
C. Both accelerate towards each other but acceleration of B is greater than that of A.
D. Both accelerate to wards each other but acceleration of B is smaller than that of A.

Answer

To solve the problem, we need to analyze the situation involving the two astronauts A and B, who are connected by a rope in free space. Here’s a step-by-step breakdown of the scenario:

### Step 1: Understand the Forces Acting on the Astronauts
- Astronaut A has a greater mass (mA) than Astronaut B (mB).
- When A starts pulling the rope, a tension (T) is created in the rope.
- According to Newton's third law, the tension in the rope will act equally on both astronauts.

### Step 2: Apply Newton's Second Law
- For Astronaut A:
\[ F = m_A \cdot a_A \implies T = m_A \cdot a_A \quad (1) \]
- For Astronaut B:
\[ F = m_B \cdot a_B \implies T = m_B \cdot a_B \quad (2) \]

### Step 3: Relate the Accelerations
- From equations (1) and (2), we can express the accelerations in terms of tension:
\[ a_A = \frac{T}{m_A} \quad (3) \]
\[ a_B = \frac{T}{m_B} \quad (4) \]

### Step 4: Compare the Accelerations
- Since mA > mB, it follows that:
\[ a_A < a_B \]
- This means that Astronaut B will accelerate more than Astronaut A.

### Step 5: Conclusion
- As a result, when Astronaut A pulls the rope, Astronaut B will accelerate toward A while A remains relatively stationary. Therefore, from the perspective of the third astronaut in the spaceship, you will observe that Astronaut B moves towards Astronaut A.

### Final Answer
- The correct observation is that Astronaut B accelerates toward A while A remains stationary.

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