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If someone dropped a feather onto a dense cloud, would it hold it? Or would it drop through the cloud? If it holds it, could a piece of thread rest on top of a cloud? What would be the maximum weight that could rest on top of a cloud? Could a thin wire to transmit sounds below the cloud rest on top of a cloud?

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Clouds can hold no weight at all. They are not a coherent material, but consist mostly of air, with tiny droplets of water (or ice crystals) suspended in it.

You may have experienced fog. That's a cloud that's low enough that you're inside it when you're standing on the ground. If you drop a feather or a piece of thread in a fog, they will fall just fine.

Small grains of dust would be able to stay suspended in the cloud -- but only if they're already small and light enough to stay suspended in the air without the water droplets that make it a cloud. So it wouldn't be the cloud that's holding them.

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A large solid object inside of a cloud will rise due to bouyancy if its density is less than the density of the cloud. It would be technologically challenging, but theoretically possible, for such a solid object to exist. In particular, aerogels can have a density lower than that of air; for example, aerographene has a density that's lower than the density of air by a factor of about 7.5.

However, aerogels are normally porous to air, and an air/aerogel combination has a density greater than that of air. Indeed, aerogels are so porous to air that it's arguably "cheating" to count them as being a "solid". Getting a block of aerogel to actually float in air would require something like applying a nonporous coating to the block while the block had some of the air in it evacuated, without removing so much air that the coated block would be crushed when exposed to normal atmospheric pressure. Like I said, it would be technologically challenging.

Furthermore, even if you created a solid object that's less dense than the cloud, that doesn't mean that the object would stop rising at the top of the cloud. Clouds aren't necessarily more dense than air, which shouldn't be surprising given that most clouds are up in the sky instead of on the ground as fog. Perhaps counter-intuitively, up to a point humid air is less dense than dry air, because the molar mass of water (18 g/mol) is less than the molar mass of air (around 29 g/mol).

So a picture of a solid object resting on the top of a cloud (as opposed to being supported by air currents within the cloud) really doesn't work.

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Clouds consist of aerosol water and sometimes ice particles whose masses are in the order of 1e-5, thus, clouds CAN hold such small weights as they do, but nothing in the order of a feather. Actually if one drops a feather over a cumulus, the water droplets will rime around the feather making it much heavier and fall through.

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