Pulley Systems

[aatari]

Hi guys, could someone please have a look at my solution and let me know if it makes any sense.

Homework Statement

Homework Equations

N/A

The Attempt at a Solution

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[Chestermiller]

I don't understand your notation. Can you please define what the various forces represent. And what does FT=FT=FT mean?

 

[haruspex]

Your "For 5kg" calculation appears to be showing that the mass on the table has no vertical acceleration. I think we can assume that without proof.
Your "For 1kg" and "For 2kg" calculations are ok except that you should use different symbols for the two different tensions.
As Chet notes, "F_T=F_T=F_T" is not very illuminating, and I can make no sense of the calculation which follows.