Specific Gravity and...gravity?

[drillers]

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I was working on a random q-bank question (dunno if it's EK or TBR or what) about a solid floating in water on Earth versus the moon.

The solid is floating with 8/10 of the solid submerged in the water. On the moon, how much is submerged (gravitational force less on the moon)?

more than 8/10
less than 8/10
same (8/10)

I was torn because of two different equations:

1) This equation I saw on SDN, SG= Weight/Buoyant Force

If I am not mistaken, 8/10 submerged is the same as saying a SG of 0.8

So I thought, well according to the equation, if we decrease the accel. due to gravity then we decrease the weight which decreases the SG so the answer should be less than 8/10


2) When an object floats, Buoyant Force = Weight

d x V x g = m x g

Gravity cancels out and thus gravity should have no affect on the amount of the solid submerged.


Well, I went with equation 1 and thought the SG should decrease which is WRONG.

Any thoughts to why I am off with my thinking using equation 1?

 

[ashtonjam]

Equation 1 is correct for objects that would sink. However, this object is actually floating. So instead, you set specific gravity equal to the percent submerged: density of object / density of water = volume of liquid displaced / volume object. Note that in this form of the equation, there is no gravitational constant, meaning that the same percent is submerged as before.

 

[drillers]

Ok that makes sense.

Floating: BF = mg

Sink/Submerged: SG = Wt/BF

Thanks for reminding me!

 

[gettheleadout]

As a note, changing gravity wouldn't affect a submerged object either, because the g term cancels:

specific gravity = W / B = mg / pVg = m / pV

 

[drillers]

<----------- Mind Blown...

Dunno how I missed that. But yeah, so then it doesn't matter whether the solid is submerged or floating. Accel due to gravity will not change the specific gravity