How do I approach this Moving Charged Particle problem?

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To approach the Moving Charged Particle problem, start by carefully reviewing the provided equations in the problem statement. For part (a), utilize the specific equation given to guide your calculations. It’s important to follow the structured approach outlined in the problem. Engaging with the step-by-step instructions will help clarify the process. Understanding the fundamentals of charged particle motion is crucial for solving this type of problem effectively.
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Homework Statement


The problem statement is attached.


Homework Equations





The Attempt at a Solution


How do I start this problem?
 

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You are given the equations to work with in the problem statement. For part (a), use the equation you are given.
 
yeah they actually walk you through this problem
 
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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