Buoyancy, Volumes, and Specific Gravity

[lazypremed]

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Here's the question:

If an object weighs 1000 N in water and 800 N in a fluid whose specific gravity is 1.1, what is the volume of the object?

A.
0.018 m3
B.
0.020 m3
C.
0.18 m3
D.
0.20 m3

And the answer.

Explanation:
D. The apparent weight of an object in a fluid is equal to mg – Fbuoyant = mg – rfluidVobjectg. Using the information in the question, we see that 1000 N = mg – (1000 kg/m3)Vobjectg and 800 N = mg – (1100 kg/m3)Vobjectg. Solving both equations for mg and then setting them equal to each other, we see that 1000 N + (1000 kg/m3)Vobjectg = 800 N + (1100 kg/m3)Vobjectg. Solving for Vobject, we see that Vobject = (200 N) / (100 kg/m3)g = 0.20 m3.

So, I have an issue with the way they solved this. It seems like they used Vobject in the the buoyancy formula as the object's entire volume instead of just the part of the object that was submerged. Nowhere in the problem does it say, from what I can tell, that the objects were fully submerged. Are we just to make this assumption? Or do ya'll agree with me that this problem is a bad one?

 

[mehc012]

Here's the question:

If an object weighs 1000 N in water and 800 N in a fluid whose specific gravity is 1.1, what is the volume of the object?

A.
0.018 m3
B.
0.020 m3
C.
0.18 m3
D.
0.20 m3

And the answer.

Explanation:
D. The apparent weight of an object in a fluid is equal to mg – Fbuoyant = mg – rfluidVobjectg. Using the information in the question, we see that 1000 N = mg – (1000 kg/m3)Vobjectg and 800 N = mg – (1100 kg/m3)Vobjectg. Solving both equations for mg and then setting them equal to each other, we see that 1000 N + (1000 kg/m3)Vobjectg = 800 N + (1100 kg/m3)Vobjectg. Solving for Vobject, we see that Vobject = (200 N) / (100 kg/m3)g = 0.20 m3.

So, I have an issue with the way they solved this. It seems like they used Vobject in the the buoyancy formula as the object's entire volume instead of just the part of the object that was submerged. Nowhere in the problem does it say, from what I can tell, that the objects were fully submerged. Are we just to make this assumption? Or do ya'll agree with me that this problem is a bad one?

I mean, technically they should have specified, but since it wasn't mentioned, yes you should have assumed it. There is literally no way to solve this without that assumption being made, and it's hardly a stretch. Think like the test-maker...it's not about proving you're smarter than the question, it's about knowing what they want you to select as the answer. In this case, with no specifics given, it would be wise to assume that the volume submerged of the object was the same in both fluids.