A 6.00-cm-diameter sphere with a mass of 89.3 g is neutrally buoyant in a liquid. Identify the liquid.

Video transcript

Welcome back, everyone. We are making observations about the following artifact. Here, we are told that an artifact has a radius of three centimeters or 0.03 m and we are told that it exhibits a neutral buoyancy in an unknown liquid. Now, the mass of our artifact is 168.4 g 4.1684 kg. And we are tasked with finding what is the unknown liquid. Well, what we can do here is we can find the density of our unknown liquid and then compare it to what we know. So since we have neutral buoyancy, what we can say is that the some of our forces in the vertical direction is going to be zero nuance. Do you want to acknowledge before we get started? On the left hand side of our screen, our answer choices, those are going to be the values that we strive for. So without further ado let us begin. So for our forces, what do we have? Well, we have the buoyancy force which is the density of our unknown liquid times the volume of our artifact times the acceleration due to gravity minus the weight of our artifact, which is mass times acceleration due to gravity. Now, this we know is going to equal zero because it's neutral buoyancy. So adding MG to both sides, what we get is that VG is equal to MG, which means that row is equal to MG over VG where the GS cancel out, which means the density of our own known liquid is simply the mass of our artifact divided by the volume of the artifact. So what can we do from here? Well, we assume that the shape of the artifact is spherical. So what we can do is we can find our volume given the radius. So the volume is going to be four thirds times pi R cubed. What this gives is four thirds times pi times 0.03 cubed giving us 0. m cubed. Now that we have found that we are ready to find the density of our unknown liquid. This is gonna be the mass of our artifact 0.1684 divided by 0.000113097. Wait, what is this equal to? Well, this gives us 1489 kg per meter cubed. Now, at room temperature, this is closest to our density for chloroform. Now the density of chloroform is 1490 pretty close to 14 89 which gives us a final answer choice of a. Thank you all so much for watching. I hope this video helped. We will see you all in the next one.