Three balls of equal mass are suspended from a thread and two springs of the same elasticity so that the distances between the first and second ball and the second and third are the same (fig.). Thus, the center of gravity of the whole system coincides with the centre of the second ball. If the thread supporting the top ball be cut, the system will fall and the acceleration of the system's centre of gravity will be 
= g
(according to Newton's second law, the acceleration of the centre of gravity of a system equals the sum of the forces acting on the system from outside divided by the system's total mass). But spring I will pull the second ball upwards with greater force than spring II will pull is downwards (the force of spring I at the initial moment f 10 = 2mg, while the force of spring II at the initial moment f 20 = mg) and therefore the centre of the second ball will have, at the initial moment, an acceleration of less than g. And yet the centre of gravity of the whole system must move with an acceleration of g the whole time. Explain the contradiction.
Text Solution
Verified by ExpertsA
Step 2: The force from spring I (upward force - 2mg) and spring II (downward force - mg) must be analyzed. When the system is initially released, the upward force acting on ball two becomes less than the downward force due to the mass of both balls below it.
Step 3: Although spring II pulls down with mg, the net force acting on the second ball will still allow the entire system's center of gravity to move with an acceleration of g, as the external forces acting on the system result in a net force of mg downwards (when considering the entire system at once).
Therefore, the initial contradiction arises from misunderstanding the independent movement of individual components versus the collective movement of the center of mass, but the center of gravity indeed accelerates at g due to gravitational force acting on the entire system.
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