Sorry for bad english[/B]
There is serie of mass and pulleys. We Know we have more than two masses. System is balanced.We take m(m<<1) from on of the masses and add to another one.
a) prove all the masses except these two have downward accleration
b) prove mass with heavier has accleration downward and mass with lighter has accleration upward
c) prove that all acclerations are relevant to m^2
The Attempt at a Solution
a) First System is balanced and when we take m out of one mass there will be accleration => speed of center of mass will increase => potential energy of center of mass will reduce => center of mass has downward accleration => T is Force that connects pulleys to wall and M is sum of all masses T<MG I dont Know how to prove this for all the masses individually.
b) since all the mass except two masses have downward acclerations and length of rope is constant one of two masses or both of them must have acclerations upward. Heavier mass is going down relevant to lighter mass but I dont know how to prove (b)