PhysicsLAB AP Free Response Question
2012 B3

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A glass U-tube with a uniform diameter of 0.850 cm is used to determine the density of an oil. As shown in the figure below, a 24.5 cm column of water balances a 27.2 cm column of the oil so that interfaces A and B of the mercury with the other liquids are at the same height. The density of water is 1.00 x 103 kg/m3.
 (a) Calculate the density of the oil.

 (b) Calculate the absolute pressure at B, the interface between the water and the mercury.

A new tube, identical to the U-tube except for a cone shape on the left, as shown below, is filled with the same volume of mercury that was in the U-tube. The mercury is at the same height on both sides of the new tube as it was in the U-tube, as shown by the dashed line. The same volumes of oil and water that were in the U-tube are now poured into the new tube, on the left and right respectively.
(c) Indicate the new position of B relative to A. Justify your answer.

____ Above A
____ Below A
____ At the same height as A

(d) A small piece of wood with density less than that of the oil is placed so that it floats in the left side of the tube. Indicate whether the pressure at the bottom of the tube increases, decreases, or remains the same.
____ Increases
____ Decreases
____ Remains the same

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