Comparing the Heights of Water and Gasoline Columns in an Open U-Tube

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In an open U-tube, the height of the gasoline column will be lower than that of the water column due to the difference in densities, with water being denser than gasoline. To balance the pressures, a greater height of gasoline is required to equal the pressure exerted by a shorter column of water. Given that the height of the water column is 15 cm, the height of the gasoline column can be calculated using the density ratio. The discussion highlights the importance of understanding fluid mechanics and pressure balance in different liquids. This problem illustrates key concepts in physics regarding fluid density and pressure equilibrium.
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Homework Statement


In an open U-tube, the pressure of a water column on one side is balanced by the pressure of a column of gasoline on the other side. (a) Compared to the height of the water column, the gasoline column will have (1) a higher, (2) a lower, or (3) the same height. Why? (b) If the height of the water column is 15 cm, what is the height of the gasoline column? [College Physics – Wilson, Buffa, Lou]

Homework Equations


I guess p=force/area?
or maybe not?
maybe

The Attempt at a Solution


I'm really not even sure what this problem is asking...I can't picture the picture that they're trying to depict. If someone could just point me in the right direction, I'd be grateful. Not looking for easy answers, I just don't have a clue what they're asking for really...
Edit:
rereading the problem My guess is that the answer to A) is that gasoline will have a higher column. To be applying the same amount of pressure their forces have to be the same and the density of water is greater (1x10^3) than gasoline (726 kg)? So just assuming you'd need more to get a greater force to equalize the pressures?
 
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They've got a U shaped tube and put water in one side and gasoline in the other side.
Your equation is correct - the force is provided by gravity... since the two liquids are different densities, what does this mean about the amount of each needed for the balance?
 
Thread 'Correct statement about size of wire to produce larger extension'
The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...

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