What Are the Truths About the Center of Mass?

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The center of mass of an object is not restricted to round or symmetric shapes, as it can exist in irregular objects as well. It accurately represents the location of the object's total mass, and while it can be represented by any point in the object, it typically lies on the axis of symmetry if the object is symmetric. The discussion highlights common misconceptions about the center of mass, particularly regarding symmetry. Participants share their attempts to answer true or false statements related to the center of mass, correcting misunderstandings along the way. Understanding these truths is essential for solving related physics problems effectively.
sheri1987
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Center of Mass --True and False

Homework Statement



The center of mass of an object...

1.True or False exists only if the object is round.
2. True False exists only if the object is symmetric.
3. True False can be used to represent the location of the object's total mass.
4. True False can be represented by any point in the object.
5. True False lies on the axis of symmetry if the object is symmetric.

Homework Equations



I basically used my knowledge to make an educated attempt at this problem, but I am still getting it wrong can you guide me to figuring it out.

The Attempt at a Solution



I put ...1) False, 2)True, 3)True, 4)False, 5)True
 
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Why do you think 2) is true?
 
Yeah, I guess I thought too quickly on #2, I looked back on my notes and found out the object doesn't have to be symmetric. Thanks
 
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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