A solid gold bar is pulled up from the hold of the sunken RMS Titanic. (c) The bulk modulus of lead is one-fourth that of gold. Find the ratio of the volume change of a solid lead bar to that of a gold bar of equal volume for the same pressure change.

Video transcript

welcome back everybody. We are looking at two identical cylinders here. We have cylinder A Part of my crude drawings here and we have cylinder B. Now, the only difference is that cylinder A is made of nickel and cylinder B is made of brass. Now we are told that the bulk modulates of nickel and therefore the bulk modulates of cylinder A is 1.7 times 10 to the 11th pascal's. And we're told that the bulk modular of brass, therefore the bulk modulates of cylinder B is 6.0 times 10 to the 10th pascal's. And we need to find the ratio in the change of volume for both of these cylinders as they are both dipped into identical vats of oil. Well, we know that the change in pressure for, you know, a given cylinder is just going to be the negative of the bulk modulates times the change in volume over the initial volume. Now, we are also told well, or and can assume that since we are being dipped into the same vat of oil, that the delta P for both, that's is going to be the same. So let's go ahead and set up two equations here that are both equal to delta P for each cylinder. Right, so delta P four cylinder A is just going to be the negative bulk module. List of a, times the change in volume of a, times the initial over the initial volume of A. And then the delta P for cylinder B is negative bulk modulates of B times change in volume over initial volume of B. Now, like I said, since the delta P. S are the same, we can set each of these equations equal to each other and these uh initial volumes are going to disappear since those are also the same. And we are left with this, we are left with that are desired ratio. The change in volume of A over the change in volume of B is equal to the bulk modules of B over the bulk modules of A. So let's go ahead and plug in those values here that the bulk modulates of B. Or brass is six times 10 to the 10th pascal's over bulk modulates of A or nickel, which is 1.7 times 10 to the 11th pastels, giving us a ratio of 0.35 corresponding to answer choice B. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.