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- [Instructor] How do you decide whether something is going to float or sink in water or any liquid for that matter? Now I should think, well, that's very simple. If something is very light, it's going to float. If something is very heavy, it will sink. But that is wrong. Because we know, for example, ships, which are very heavy, made of metal, can float on water. Yet something like a spanner or a nail, which could be made of the same metal, which is very light compared to the ship, can easily sink. So it's not their weights that decide whether something will float or sink. Then what does? Turns out, it's their density. And so, in this video, let's logically figure out, why doesn't it depend on weight, but it depends on density? So let's imagine I take a chain of gold and put it in water. I want to know whether it's going to float or sink. How do I do that? Well, since it's gold in water, you might already know what's gonna happen. But let's say we didn't know. How would I figure it out? Well, I have to first think about the forces acting on it, right? I mean, if I knew that it's being pushed up, then it's gonna try and float. If it's being pushed down, it's gonna sink. So let's think about the forces which are acting on our chain of gold. One force that we might be familiar with is its own weight. Because of gravity, it has its own weight that's pushing it down. Is there any other force acting on it? Yes, there's a buoyant force. Water is pushing up on it. You've seen before that when you put any object in a liquid or gas, in fluids, they have a natural tendency to push up on those things. We call that as the buoyant force. A man called Archimedes tells us that that buoyant force acting on that object equals the weight of the fluid that it displaces. So basically, before this gold chain came over here, that space was occupied by this water, right? Now when the gold chain comes over there, that water has to move away, making space for that gold chain, isn't it? The water that moves away is what we call the displaced water. It'll actually go up, and the height of the water will increase. But I'm just, you know, moving it over here so that we can see that displaced water. Archimedes tells us that the buoyant force equals the weight of this displaced water. So we can think of it as the weight of this chain of water. So whatever is this weight, that much will be the buoyant force. If you need more clarity on why this is true and everything, we've talked a lot about Archimedes' principle and buoyancy in previous videos. So good idea to go back and check them out. Anyways, now we can see it all boils down to figuring out which of these two is heavier. Because if I think this one is heavier, if the chain of, water chain was heavier than this, then this force would be heavier. It would be larger. As as result, our gold chain would float. On the other hand, if the chain itself was heavier than the chain of water, then our gold chain would sink. So you see, it's all now. Now it's all about figuring out which one is heavier. If this is heavier, it'll float. If this is heavier, it will sink. So which one do you think is heavier, a chain of water or a chain of gold? Now again, you might know the answer to this. But let's say we didn't. Let's say I had no clue. How would I figure this out? Well, one way to do that is by looking up the density of gold and water. What's density? Density is a number which tells us how much something weighs per unit volume. Here, let's take an example. It'll make a lot of sense. So if I were to look up the density of gold, it would give me something like this. The symbol stands for density. It would say the density of gold is 19 grams per centimeter cubed. Now what does it mean? This could mean that if I were to take one centimeter cubed of gold, so imagine a tiny box of one centimeter cubed completely made of gold. That would weigh 19 grams. That's what it says, 19 grams per centimeter cubed. Now it doesn't have to be a box. It can be any shape you want. As long as you take one centimeter cubed chunk of that gold, it'll always be 19 grams. That's what this number is telling us. So let me just get rid of that. So now I know. Every centimeter cubed of this gold chain weighs 19 grams. What about water? Well, we can look up the density of water. It turns out to be one gram per centimeter cubed. Ooh, this means every centimeter cubed of this water weighs one gram. Every centimeter cubed of this gold weighs 19 grams. So can you tell now which one is heavier? I'm pretty sure you can. It's the gold. Because gold is heavier, it's weight will be larger. As a result, our gold chain is going to sink. All right, let's take another example. Imagine I took a big box of wood. It's just not a hollow box. It's completely filled with wood. Let's imagine a solid box of wood, very heavy. Now again, I want to figure out whether this is going to float or sink. What to do? We'll do the same thing. Let's look at all the forces. We know it's being pushed down by its own weight. This time, this is much heavier than the gold chain because I'm taking a big box of wood. Imagine that. I got into Archimedes' principle. It's going to displace an equal amount of volume of water, the same shape you can see, a box of water. It is going to get pushed up by a buoyant force which is the same as the weight of this water. Now again, to figure out whether this is going to float or sink, I need to know which of these two weights is more. I already know that water, for every centimeter cubed it weighs one gram. Now I want to know, what about the wood? How much does it weigh per centimeter cubed? So again, I can look up the density of wood. The density of wood turns out to be .7 grams per centimeter cubed. Ooh. So every centimeter cubed of this box weighs .7 grams. Every centimeter cubed of this box, which has the same size and shape as this, but every centimeter cubed of that weighs one gram. So which one weighs more? Can you pause the video and think about this? I'm pretty sure you can think about this. So it's clearly. It's this water is more now this time, right? The box of water will weigh more. Because of that, that means our buoyant force, this weight will be larger than the weight of the box. As a result, our box will float. So right in front of our eyes, we're seeing that weight doesn't decide whether something will float or sink. We are having an extremely heavy object which is floating, an extremely light object which is sinking. Why is that happening? Because we're seeing that something which is extremely heavy can displace even heavier amount of water which is why it is floating. Something which is light is displacing even lighter amount of water because of which it is sinking. So you see, the secret to floating is that your object should be able to displace even heavier amount of water. When will that happen? That can only happen provided per centimeter cubed, your object is lighter than water. Otherwise, it'll sink. So the secret to floating is per centimeter cubed, objects should be lighter than water. In other words, the density of the object should be smaller than the density of the water. Then it will float. You see, okay? So the water, if you want to figure out whether something's gonna float or not, calculate its density, and check whether it's lighter than water. So in general, the floating condition is, the density of the object should be smaller than the density of the fluid. It's not just for water. It can be for any liquid or gas. By the way, how do we calculate density? Well, the density is usually calculated as mass divided by its volume. You see, mass divided by volume gives you the density of that object. As long as it's smaller than that of the fluid, it will float. Of course, if you need more clarity on this, where this comes from, we've talked a lot about that, density in previous videos. So great idea to go back and watch videos on density. Anyways, now we can answer our original question. So why is it that if I put a spanner, it will sink? A spanner is made mostly of steel. Steel has a density of eight grams per centimeter cubed, roughly, which is way more than that of water. That's why, if you put it in water, it's going to sink, larger density than water. On the other hand, what about a ship, a ship which is made of the same material? Why doesn't that sink? Even it should be heavier than water per centimeter cubed, right? No, it's not. Because a ship is not completely made of metal, not completely made of steel. Unlike the spanner, a ship has a lot of empty space in it. Because of that, the metal occupies a much larger volume. Just think about it. I take that metal, and I put a lot of empty space in between. I increase its volume. The density starts decreasing, right? That's the secret for ships. They have a huge volume. So if you take the mass of this entire ship and you divide by its volume, you will find that its overall density will still be smaller than that of water. That's the secret, okay? So ships have a density smaller than that of water. That's why, if you put them in water, they will float. So long story short, what did we learn? We saw that if an object needs to float in water or any liquid for that matter, it needs to be able to displace an amount of liquid which is heavier than the object itself. That can only happen provided per centimeter cubed, the object is lighter than the liquid. It's for that reason, in order to float, the object needs to have a smaller density compared to the fluid. On the other hand, if the object has a larger density than the fluid, like gold in water, it will not be able to displace the amount of water equal unto its weight, and it will sink. Hey, what could happen if the object has the same density as that of the fluid? I'm pretty sure you can figure that one out yourself.