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 ?
- A.The centre of mass of the system moves towards Y.
- B.X moves and the centre of mass of the system follows him.
- C.The centre of mass follows the tool.
- D.The centre of mass remains fixed.
Correct answer
Explanation
The correct answer is D, the centre of mass remains fixed. With no external force on the system, its centre of mass cannot start moving.
The throw is an internal force: X pushes the tool forward and the tool pushes X backward with an equal and opposite force (Newton's third law). The total momentum of X, Y and the tool was zero before the throw and stays zero after it. Since the velocity of the centre of mass equals total momentum divided by total mass, it stays at rest. The tool moves towards Y while X recoils the other way, and their mass-weighted positions balance out.
A is wrong because moving the centre of mass towards Y would need an external push in that direction.
B is wrong because X recoils, but the centre of mass does not follow any single body.
C is wrong because the tool's forward motion is cancelled by X's backward recoil.
Exam tip: internal forces can move the parts of a system but never its centre of mass.
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