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If that is not the case, can someone please help me out in understanding the movement of the pulleys which is leading to a different ratio of acceleration?

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  • $\begingroup$ Do the pulleys have mass? $\endgroup$ – Luo Zeyuan Nov 19 at 3:08
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    $\begingroup$ Does this answer your question? Pulley system, what is the ratio? $\endgroup$ – sammy gerbil Nov 19 at 3:17
  • $\begingroup$ The ratio of accelerations or velocities is the same as the ratio of distances moved. (See definition of velocity ratio.) The masses are irrelevant. $\endgroup$ – sammy gerbil Nov 19 at 3:21
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    $\begingroup$ This problem is weird. There are two parameters, which you can take to be the heights of m1 and m2. If everything else is massless and frictionless then the Lagrangian should just be the sum of the kinetic-potential energy of m1 and m2, so they're completely independent as long as there's enough rope. It reminds me of the infamous plane-on-a-treadmill problem. I don't want to answer because I feel like I'm missing something. $\endgroup$ – benrg Nov 19 at 4:36
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    $\begingroup$ The left pulley reminds me of a 'fools pulley', not sure if it is relevant here $\endgroup$ – Luo Zeyuan Nov 19 at 4:54