Elevator + Counterweight problem

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The discussion revolves around a homework problem involving an elevator and counterweight. A student seeks verification of their solution, which is confirmed as correct by others in the forum. It is suggested that solving the problem symbolically first, before plugging in data, would save time and simplify the process. The student acknowledges this advice and expresses intent to adopt this method in future problems. The conversation highlights the importance of symbolic solutions in physics problem-solving.
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Homework Statement


The problem is as posted in this picture[/B]

Hey guys/girls, my teacher gave us this problem which I am not sure if I have correct. Could someone please verify if my solution is correct.
6qw8kl.jpg

Homework Equations



As in my attempt

The Attempt at a Solution


My attempt is scanned -
swpnaf.jpg
 
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Welcome to PF!

Your solution is correct, but you save time both for yourself and for the helpers if you do the solution symbolically, and plug in the data at the end. You would see that the radius of the rotor cancels.
 
ehild said:
Welcome to PF!

Your solution is correct, but you save time both for yourself and for the helpers if you do the solution symbolically, and plug in the data at the end. You would see that the radius of the rotor cancels.
Thanks!
Ok, I will do it symbolically next time
 
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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