How do we determine whether circuit element is negative or positive?

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Homework Statement
How do we determine whether this element in circuit is negative or positive(Nodal analysis)?
Relevant Equations
Nodal analysis
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Aren't the +- signs on the selected voltage source enough?
 
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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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