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Vicwe Policles Oltremt Attcmgc072-KE metal sphere ~catc unatrained Icneth)verticii doceocn Iromgustretchas (rom0 12 M(o023m (relstlvo Hmu comtant arNumbeteTextbook ...

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Vicwe Policles Oltremt Attcmgc072-KE metal sphere ~catc unatrained Icneth)verticii doceocn Iromgustretchas (rom0 12 M(o023m (relstlvo Hmu comtant arNumbeteTextbook and Mcdia:GO Tutorial HerlntrU muluple altee auuccn

Vicwe Policles Oltremt Attcmgc 072-KE metal sphere ~catc unatrained Icneth) verticii doceocn Iromgu stretchas (rom0 12 M(o023m (relstlvo Hmu comtant ar Numbet eTextbook and Mcdia: GO Tutorial Herlntr U muluple altee auuccn



Answers

A uniform sphere has mass $M$ and radius $r .$ A spherical
cavity (no mass) of radius $r / 2$ is then carved within this
sphere as shown in Fig. 32 (the cavity's surface passes
through the sphere's center and just touches the sphere's
outer surface). The centers of the original sphere and the
cavity lie on a straight line, which defines the $x$ axis.
With what gravitational force will the hollowed-out sphere
attract a point mass $m$ which lies on the $x$ axis a distance $d$
from the sphere's center? [Hint: Subtract the effance $d$
the "small" sphere (the cavity) from that of the larger entire
sphere. $]$

Here. We have two dates. Both are what do the charge? So the electric field times in the upward prediction over the top that it boys down the ward under the bottom played and in the center we have

We have three small spheres and we're going to melt them down to create a large sphere with an unknown radius. Now enter. To find the radius of this large sphere, we need to know its volume and energy. No, it's volume. We need to know the volumes of the spheres that were put into it. So each of these small spheres has a given volume which is given by the formula for volume of a sphere. 4/3 Hi are cubed where R is the radius. And so when you add up the volumes of all of these small spheres, you will get the volume of the large one. Thus, let's figure this out. The volume of the big sphere is going to be 4/3 pi times two cubed plus 4/3 pi times three cubed plus 4/3 pi times four. Cute. Okay, we can factor out of 4/3 pi from all of the's. Giving us 4/3 pi times to cube is eight plus three cubed eyes 27 plus four cube is 64 and this can simplify to 4/3 pi times the sum of all those are 99. Okay, so that's the volume of all three of the smaller ones added up Well, once we add all those up, we're going to shape them into the big sphere so we can set this equal to the big spheres value. Thus 4/3 pi times 99 is equal to 4/3 pie times X cubed where X is the radius of the big sphere. We can cancel the 4/3 pi from both sides. That's why didn't multiply it out. I want to cancel later. Leaving us with just X cubed equals 99 and when you take the cube root of both sides, you'll get your answer of X is equal to about 4.6 with just a little bit of rounding. Thus, the big sphere is going to have a radius of 4.6 millimeters.

So let us determine the volume of copper. So again, volume of corporate equals mass divided by density. We have both the values substituting the values we have 77.5 Grand for mass and density is eight 96 from per Centimeter Cube. And the volume turns out to be 0.8 37 centimeter cube. Now for the 2nd 1 We need to determine volume of silver using the same formula mass divided by density Mass is 92.5 g And density is 10.5 gram per centimeter cube. The volume turned out to 3 8.81 centimeter cube. No, for the volume of sterling silver, volume of stolen silver will be Volume of seven 5% copper. Yes, volume of 92.5 silver. Yeah, substituting the values, we have 0.837 Centim cube plus eight point 81 centimeter cube. The answer turned out to be 9.65 centimeter cube.

Thank you in this solution that given that is that is equation of the sphere is given. Yeah. Yeah that is exit square. Yeah plus y squared plus jerry square Plus two X -2 X 3- to jail this equal to -1. And now in the question it is saying that we have to find center and radius of despair. Yes. So this is the infusion. Now I will try to answer the execution. So in the cell first I will write the human equation again. That is X squared plus y square plus jerry square plus two X minus two is equal to minus one. No, my next step is rearranged the human equation so it will be return is that this X squared plus two X then plus y squared plus jerry square minus to jail Is equal to -1. No next step is we have to add one. What in a world where entities and uh uh huh We have to add 12 times in the right side. Yes. So after doing this it will be written a series in the first parenthesis. I had to add one. So do you return to studies? X squared plus two X plus one then plus y square. Now here in the second point this is I will add one. Yeah. So it will recognize there is J D squared minus two dead then a plus one. Yeah it's equal to minus one. And on the right side I have to add 12 times. So I do originals. There is plus one plus one. No, that's your babies. I can see that it will be recognized. That is X plus one. Ball is square then plus y square Plus debt -1. Only square Is equal to one. So you can see that I had to get the square of each variable. So no. My next step is I will write the standard forum extended equation of Israel so that is x minus X. Not wholly square place. Why minus? Why not all the square plus? They're managed did not. All the square is equal to our square and centuries. That is X not comma, why not comma Janet and radius is equal to our. So my next step is compared the resulting equation with this extended equation of his pair. So I will get the center of even equation that is coordinator of center is that is minus one comma zero coma one. So here I have got the value of X not why not? They're not by comparing so and similarly areas will be returned as that is, Is carried out of one. So it means one. So this is a sort of given fusion. Thank you.


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