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SHM of liquid in U tube

  1. Apr 10, 2014 #1
    The figure shows a U tube of uniform cross-sectional area A containing liquid of density p. The total length of the liquid column is L. When the liquid is displaced by an amount x from its equilibrium position, it oscillates with simple harmonic motion.

    The weight of liquid above AB provides the restoring force. Write down an expression for the restoring force.

    My answer: pAgx

    Book's answer: 2pAgx.

    Why is there a 2?

    I think it's not just the liquid above AB, but the liquid column below AB which is higher than the liquid level in the left side arm is also providing the restoring force. But the question only says above AB. I am confused.

    Please shed some light on this, thanks.
     

    Attached Files:

  2. jcsd
  3. Apr 10, 2014 #2
    Don't be confused. Your interpretation is correct. The important point is the level difference. One side move x up while the other side moves x down giving a level difference of 2x.
    By the way, I doubt the density is p. It's probably ρ. That letter is called Rho. You should learn the name of the Greek letters and how to tell them apart from Latin letters.
     
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