Rolling pendulum angular acceleration

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To solve the problem of rolling pendulum angular acceleration, it's essential to demonstrate an attempt at a solution. Participants are encouraged to reference specific methods taught in their module related to the topic. Sharing any preliminary work or calculations is crucial for receiving targeted assistance. Clarifying any remaining questions will help facilitate a better understanding of the concepts involved. Engaging actively in the problem-solving process is key to mastering the subject.
YaniHozya
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Homework Statement
My lecturer is absent and hasn't been replying to my emails, and im unable to find much online about pendulums on trolleys so i would much appreciate any advice or help on how to do this question.
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You have to provide an attempt at a solution.
 
Welcome, YaniHozya!
What are those methods taught in the module that the question mentions?
Please, show us any work that you have done so far, or ask about things that you still don't understand.
 
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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