How do I find the centre of gravity of this object?

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To find the center of gravity of the object for stability in water, the discussion highlights confusion regarding the correct value, with one participant suggesting it should be 1.5 meters instead of 1. The problem states that the center of gravity is 0.5 meters above the water surface, leading to a total height of 1.5 meters from the bottom of the object. The height of the barges and platform is also crucial for accurate calculations. Clarification on these dimensions is necessary to resolve the discrepancy in the center of gravity assessment.
ipocoyo
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Homework Statement


Hi everyone, I need help finding the centre of gravity for this object in order to find its stability in water. However, I am having trouble finding out the centre of gravity.

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Homework Equations



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The Attempt at a Solution


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The answer says that it is 1, but shouldn't it be 1.5? 3/2 = 1.5
 
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We need to know the height of the barges and the height of the platform, however the statement says that the center of gravity is 0.5 above the surface of water, that is d+0.5=1.5m from the bottom of the object.
 
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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