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The definition I use are the following. An extensive quantity is proportional to the number of components in the system it qualifies. If you double the number of components of the system (by doubling the number of atoms, the volume of liquid...), its extensive quantities will double too. On the opposite, an intensive quantity is always in a way or ...

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Basically, displacement applies. Although the weight of the crown remains the same, the force (or heft) doesn't. What happens is that the weight displaces a volume of water, and this displacement of water is what makes the force lesser. So it needs fewer weights to balance it on the other side. If $C_a$ is the weight in air, and $C_w$ in water, the ...

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What you have here is the relative density of the substance with the fluid. We can have standard value for relative density of pure gold with that fluid. And easily compare. Here I think the fluid could be water, standard relative density of gold is 19.3, we got it 11.3,hence not gold !

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Consider $w$; it's the volume of the object times its density times $g$. Consider the buoyant force; it's the volume of the object times the density of the fluid times $g$ So, what's the ratio of the weight to the buoyant fore, when you cancel out the constant factors?

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You have to put net force to zero. I think that the problem is that you use the same volume for the two formulas. In one you have the entire volume, in the other only the volume in the water.

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Tungsten has been known to bait gold bars (historically). There are a few methods we use to determine if something in front of use is gold or if it is alloyed, or if its plate, fill or scrap. You can cut the bar in half...You will then know immediately of you got bunk gold. You can do a specific gravity check of your gold. There are scales designed for ...

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The trouble is that your table, or whatever object it is, will act as a waveguide. That's because the sound waves will (partially) reflect of the wood/air surface then travel back into the table and interfere with other waves. The result is going to be hideously complicated to calculate. As Luboš says in a comment, if the thickness of the table is much less ...

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