Calculating Speed of Falling Meter Stick

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To calculate the speed of the center of mass of a falling meter stick, energy conservation principles can be applied to both scenarios. In the first case, the stick falls freely, and potential energy converts to kinetic energy as it drops. In the second case, where one end remains in place, the rotational dynamics must be considered, as the stick pivots around the fixed end. The center of mass speed can be determined by analyzing the energy transformations in each situation. Understanding these concepts is crucial for solving the problem effectively.
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First let me say I appreciate everyone on these forums who takes the time out to help.

My question is as follows:
It has 2 parts.

Part 1:
A uniform meter stick (1 m long) is held on its edge against a frictionless table. The meter stick is released and it falls to the table.

Part 2:
The meter stick is connected so the stick can still fall but one end remains in place.

This is all the information I have and I am suppose to figure out the speed of the center of mass.

I am completely lost as how to do this.
Any help or guidance would be extremely beneficial. Thank you.
 
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Hint: Both cases can be solved using energy conservation.
 
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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