 I just imagine you are stuck in such a storm. So I'm here to tell you there's nothing to worry much. Physics is at your rescue guys. Let us see how physics will help us and we should not worry that much. So just ignore this sinking ship. Your ship is not going to sink because physics is at your rescue. So let's talk about the basics which are there in play. So to understand how the ship will not sink, so we need to first define some reference points which we'll be using to define the stability of the ship. So just keep a note of it. We'll be talking about the gravity here. We'll be talking about buoyancy and there is probably a new term for you guys and that is metacenter. So before I even talk in a very technical way, let me quickly introduce them or define them. So gravity is a point which acts as if entire weight of the ship acts through it. Alright guys, the buoyancy point is a point which is nothing but the centroid of the submerged portion. So we have learned quite a bit about the gravity. We know that it will act through the center of mass. Okay? However, the buoyancy force, what we have learned, this is nothing but a buoyant force. Formula for that, we learn in grade 9th as well as in grade 11th. Right? We know that whenever something is partially or completely submerged in a liquid, the liquid will apply an upward thrust and this is that buoyancy force. So just like gravity can be acted as if it is acting through the center of mass, Similarly, buoyancy also, there will be a point which will act as if the buoyant force is acting through it and that point, my dear friends, is the centroid of the submerged portion. Alright? So, there will be a centerline here. This is the centerline. Okay? Line of symmetry, we call it. I hope you understand what is buoyancy and the gravity force here. There is something that we will take up in the subsequent slides. Alright? So let us proceed. Now, what you see here, I have taken a small boat here, okay, which is floating horizontally, let's say. Okay? Here you can see the center of mass. This is the center of gravity and the submerged portion is symmetrically distributed on the left-hand side and on the right-hand side. So, the center of buoyancy through which the entire buoyant force will act will be on the cell line of symmetry only, which is the centerline. Okay? So this is on a calm water body. But what if there is a storm and your boat turns a little bit? If the boat turns, let us say in the given direction, you can see there is more portion on the right-hand side. So naturally, the centroid of the submerged portion will shift on the right-hand side and your buoyant force will act through this point, which is the centroid of what? It is the centroid of this portion, which is submerged. Okay? So now, what will happen? Clearly, you can see there will be a rotation happening, isn't it? If you look at this center of mass through this point, this force will try to rotate it back to its original position. Okay? So, basically what I can say, since there is no upward motion, there is no upward acceleration as such, we can say that gravity force is equal to the buoyant force. But in this case, there will be a rotation back to the original position. Okay? So, the situation is something like this, my dear friends. It is like this. You have a rod, let us say and the two ends, there are, let us say, springs, okay? If you try to rotate this rod, the rod will take up this kind of shape. But the force from this spring is downward. The force due to that spring is upward. So, as soon as you leave it, it will try to go back. So, that is what is happening here. There is a spring-like action over here, which tries to go back to its original shape or which tries to make sure that the boat goes back to its original shape. All right? So, let us take few more variations here. Look at this. In this case, look at what is happening. The boat has tilted so much that the center of the buoyant force is shifting on the left hand side. Now, the buoyant force is acting through here and the gravity force is on the right hand side of the buoyant force. Now, tell me, will this buoyant force help the boat to go like this or the buoyant force will try to rotate the ship like that? Exactly. Now, the buoyant force is not helpful. The buoyant force will further topple the ship. So, whatever kind of storm is there, it should not rotate it like this, okay? Now, suppose, let us take a situation just for fun. If you have a small boat like this and you went to the edge of it. Now, when you go towards the edge, what will happen? If I take you and the boat together, your center of mass will not lie on the line of symmetry because you also have some mass. So, your center of mass would probably shift, let us say, over here, which is also the point where the centroid of the submerged portion is lying. Now, this is a position, my dear friend, which is a critical position because you go a little bit this side and the boat will topple completely or if you go that side, then you will be back to the safety. All right, so I hope you're getting a little bit sense of what I'm talking about here. We will talk it in little bit more detail. So, just to take a mathematical view over it, let us consider these three situations. In first situation, you can see there is this, I'll put a red line here. This is the line of symmetry on which the center of mass is lying. And when this boat has tilted a little bit, the center of buoyancy, which is here, okay? Now, if I draw a line vertically like that, then wherever my vertical line intersects the red line, that is the meta-center, my dear friends. So now, I hope you understand what is a meta-center, all right? Now, if you take this as meta-center, then this distance g to m is important. So, mathematically, if you see here, if g to m, if you go towards g to m and m is above g, then the situation is safe situation. Or you can say positive or stable, whatever you may want to call it. In fact, it is not stable though. It is just so that it is going towards the stability after this. Because you can see this buoyant force will try to rotate it back to the safety. Over here, g to m distance is zero. So, it will remain like this until a little bit of disturbance will shift the buoyant force further this side or the center of buoyancy a little bit that side. So, that will decide the fate of that. However, in this situation where the meta-center is below the center of mass, it will not help us. It will keep it rotating and the boat will sink. So, now I hope you understand why it is called positive. This is called neutral and why this is called negative, all right? Now, here there is one important thing you can see. There is this g to z distance, all right? So, if you take this g to z distance, your buoyant force is acting through this line, all right? So, your buoyant force through the center of mass is applying a torque and this is a perpendicular distance. So, if g to z distance is there or you can say if it is positive, it is positive. I am taking g to z distance to be positive only when the z is on the right hand side of g. So, if it is positive, it implies that if this is positive, then it implies that I will go back to the safety, all right? So, now the point here is that I am taking the position of the meta-center fixed but as this angle of tilt increases, the meta-center also moves because of the construct of it. So, you can see on the other slide over here as you tilt the meta-center from here shifts there, then further tilt meta-center from 20 degree, it goes to 45 degree, it comes down here. So, like this meta-center keeps shifting its location. So, that makes this study little bit more complex but for our purpose, we will take meta-center position to be fixed. However, in real case, what happens meta-center keeps shifting and this is the kind of graph that you will observe with respect to g to z, okay? So, g to z, as long as it is positive, you can go back to the safety and there is a large degree of tilt that your boat can accommodate here, okay? So, you are safe in a storm till you are rotated by a tremendous angle, let us say 80 degree or 70 degree, something like that, okay? So, don't worry when you are a ship and the storm is shaking you up, just keep calm, right? So, thanks for watching the video. This is Dheeraj from Centrum Academy, signing off.