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Assume massless pulleys and strings. Going from up to down, pulleys are labelled 1,2,3,4.

I am trying to grasp how tension is passed from string to string. My intuition tells me that starting downwards the tension is T is both sides (pulley 4),then for pulley 3 the tension is now T/2, then for the pulley 2 it is T/4 and because the string of pulley 1 and 2 is the same the tension is T/4 on the mass above. However as the number of pulleys increase to infinity the mass in the bottom should have an acceleration of zero so is it the inverse ? Tension decreases going downwards?

I have to Work out the individual acceleration of the two masses, and the value of the tension in the string.

Why does the question mention the string ? Aren't there multiple strings ?

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For a massless pully and massless strings, the tension in the string is the same on both sides of a pully; this is not true if the inertia of the pully is considered, but you are told to assume massless pulleys. The tension in the strings can be different for each pully. You need to do a force balance on each mass and on each pully (hint: the pulleys have no mass), with the length of the strings as a constraint. As this may be a homework problem, you need to work out the details yourself.

You can find discussions of a similar problem on the internet under "Atwood machine".

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