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#1 2012-10-10 15:16:48

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,229
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Floatation

An object floats in water such that one-fifth of its volume is above the surface of water.
The same object floats in another liquid such that one-twentieth of its volume is above the surface of liquid.

Find the relative density of this liquid

Please explain me step by step, this chapter is quiet confusing to me


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'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#2 2012-10-10 19:29:12

bob bundy
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Registered: 2010-06-20
Posts: 6,092

Re: Floatation

hi Agnishom,

When an object floats in any liquid, the weight of liquid displaced = the upthrust on the object.

example.  ice is less dense than water.  The RD is about 0.91

An ice cube of 1 cubic centimetre is put in water.  It's weight = volume x RD = 0.91 g

So 0.91 g of water is displaced (pushed out of the way as the cube settles down in the water).  So 91% is below the waterline and 9% above.

But the RD is relative.  Because it depends what liquid you use as the reference that you measure other substances by.

If we lived on a liquid methane planet, we'd probably use that as the reference!

On this planet we usually use water as the reference and we have rigged the units so that 1 cc of water weighs 1 g; giving  water itself a density of 1.

Water will float on a heavier liquid, such as mercury.

Your example.

1/5 above the surface of the water so it's RD (= density = specific gravity)  is 0.8 

Let's say we have 1 cubic centimetre of the substance.  Then its weight is 0.8 g.

Now it is placed in another liquid and it floats with just 1/20 above the surface. 

That means it displaces 0.95 cc of that liquid and that amount of liquid must weigh 0.8 g (in order to hold the substance up).

So the density (specific gravity) of that substance (relative to water) must be = weight / volume = 0.8 / 0.95 = 0.84


Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2012-10-11 04:01:11

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,229
Website

Re: Floatation

Thank You smile
However, I think you should have said: Density = Mass/Volume


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2012-10-11 04:08:34

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Floatation

Ok you're right that would be mass.

And I thought I was pedantic!   smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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