specific gravity

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mR LaZy

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I have a practice question which i don't get

floating object is 75% submerged in water and 50% submerged in CCl4, what is the specific gravity for CCl4

a.4
b.1.5
c.0.67
d.3.00

the answer is b. 15

how is that?

thanks
 

silverlion

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before getting into the solution to your question lets just get some background:
To put it in simple terms, specific gravity is the factor by which something is denser than water.
If there is an oil that has a mass of 2 KG/1000 ml then as compared to water (which is approx. 1kg/1000 ml) the oil is twice as dense and therefore the oil has an S.G. of 2.

Now, in your question, just equate the weight of the liquids displaced (this is because the weight of each liquid displaced will be the same as the weight of the object). An object floats in a solution when it displaces an amount of the liquid that is equal to its weight.

Let the weight of the object be Wo.
Let the total volume of the object be Vo.
The density of the object be Do
Density of Water is Dw and that of CCl4 is Dc.

So in the case of the object floating on water, volume of water displaced is 0.75*Vo
So, Wo = 0.75*Vo*Dw.................1

Similarly, In the case of CCl4, Volume displaced = 0.5 * Vc
again Wo = 0.5*Vo*Dc..................2

Equate 1 and 2

So, 0.75*Vo*Dw = 0.5*Vo*Dc

Specific gravity of CCl4 is Dc/Dw = 0.75*Vo/0.5*Vo

Dc/Dw = 0.75/0.5 = 1.5

Sorry if I've made it look complicated...:p
 

silverlion

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BTW....this looks like a lot of calculation but when you do it most of it is done in the head...all you get is the final equation in the end.....

I think I read some MCAT prep book that said that you might as well remember the formula ....
S.G.of liquid 1 = Fraction of water displaced by object / fraction of liquid 1 displaced by same object.

Here that would be 0.75/0.5 = 1.5
 

BerkReviewTeach

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I have a practice question which i don't get

floating object is 75% submerged in water and 50% submerged in CCl4, what is the specific gravity for CCl4

a.4
b.1.5
c.0.67
d.3.00

the answer is b. 15

how is that?

thanks

Did they give you the equation sheet, review packet, and answers to those questions yet? All of those in-class questions that just have the letter key at the bottom have an answer explanation once the class is the final month. You should email Todd or ask him in class when the answers will be given out.
 

ipmed

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Did they give you the equation sheet, review packet, and answers to those questions yet? All of those in-class questions that just have the letter key at the bottom have an answer explanation once the class is the final month. You should email Todd or ask him in class when the answers will be given out.
Thanks TBR Physics. I answered correctly without having a clue of how I got there! I hope this works on the actual test
 
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