Whats the tension T' in string 1 if tension of highlighted string is T

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The discussion centers on calculating the tension T' in string 1 when the tension of a highlighted string is T. It references a previous discussion on Physics Forums regarding tension constraints and their potential to yield incorrect results. The analysis emphasizes the importance of understanding the relationship between multiple strings under tension and the implications of constraints in physics problems.

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Homework Statement
I have attached image of question as well as my attempt!
Relevant Equations
If we consider string as uniform then T'=T but if make fbd of pulley 1 the T'-2T-ma1=0 = T'=2T as m=0 for the given pulley. This is contradicting
IMG_20191027_045440.jpg
 
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