Two astronauts X and Y float in deep space, far from external forces. Initially, they are at rest relative to one another. X throws a tool towards Y. Consider the two astronauts and the tool as one system. Which one of the following statements is correct?
The centre of mass remains fixed.
The two astronauts and the tool form an isolated system since they are far from all external forces. Before the throw, the net momentum of the system is zero. When X throws the tool towards Y, the forces involved are purely internal to the system (X on the tool, and later the tool on Y). Internal forces cannot change the total momentum of a system, so the total momentum stays zero throughout. Since the centre of mass moves with velocity \(v_{cm} = \dfrac{P_{total}}{M_{total}}\), and \(P_{total}=0\) remains constant, the centre of mass does not move at all — it stays fixed in space. Hence option (d) is correct.
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