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Pressure

AP Physics 1· difficulty 3/5

water oil h_w h_o

A U-tube contains water (ρw=1000 kg/m3\rho_w = 1000~\text{kg/m}^3) on the left with a column of oil (ρo=800 kg/m3\rho_o = 800~\text{kg/m}^3) floating on the right. The oil column is ho=10 cmh_o = 10~\text{cm} tall. How high above the water-oil interface does the water sit on the <strong>left</strong> side (i.e., find hwh_w such that pressures balance at the bottom)?

  • A

    6 cm6~\text{cm}

  • B

    4 cm4~\text{cm}

  • C

    10 cm10~\text{cm}

  • D

    8 cm8~\text{cm}

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Explanation

Pressure balance at the same height inside the connected fluid: ρwghw=ρogho⇒hw=ρoho/ρw=(800/1000)(10)=8 cm\rho_w g h_w = \rho_o g h_o \Rightarrow h_w = \rho_o h_o / \rho_w = (800/1000)(10) = 8~\text{cm}.

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