This comes from a failure to understand the forces involved. Assuming
that it is equilibrium the load from the weighted plate will be
transferred to the pulleys at right angles to the plane of contact. This
plane of contact will be the circumference of the pulley, and any force
at right angles to it will pass through the pulley centres and no moment
(torque) will be generated.

If it is not balanced and in equilibrium, both pulleys will spin briefly
in the same direction when the plate and weights fall noisily between
them to the floor. You will have been much better off just pulling the
thing.

Basically somebody got their calcs wrong and thought they'd found free
energy.

Ron Natalie wrote:
jigar wrote:
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Jigar Patel

This is the stupidest thing i've seen in quite some time.
Case 1 uses the energy of the falling plate to offset
the work being done but ignores energy needed to raise
the plate to begin with.

While it indeed may take less energy to spin the shafts
in the former case, the overall work is a wash.

It's entirely analogous to a pulley with a rope over it with
weights on both ends. If the weights on the ends of the rope
are equal, then yes it takes less work to rotate the pulley
than if all the weight was at one end of the rope, but raising
in one case you've done some work, and the other you've accomplished
nothing.