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

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The discussion focuses on determining the tension T' in string 1, given that the tension in another highlighted string is T. It draws parallels to a previous thread that addresses similar tension-related issues in physics. Participants emphasize the importance of understanding the relationships between different strings and their tensions in a system. The conversation highlights the need for careful analysis to avoid incorrect conclusions regarding tension constraints. Accurate calculations and clear reasoning are essential for resolving such tension problems in physics.
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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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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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