Pressure Variation in Fluids questions with solutions

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• MCQmediumFluid MechanicsPressure Variation in Fluids

  Mercury is poured into a uniform vertical U-tube and water is poured in it. The level of water is the same in both arms. A piece of wood is dropped into one arm and some water, equal in weight to the piece of wood, is added to the other. Then, consider the statements: (I) The level of mercury will be same in both the arms. (II) The level of water will be same in both the arms.

  Options

  • Option A

    Both I and II are true

  • Option B

    I is true but II is false

  • Option C

    I is false but II is true

  • Option D

    Both I and II are false.

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• Multi-correctmediumFluid MechanicsPressure Variation in Fluids

  A beaker is filled in with water is accelerated by a m s⁻² in + x direction. The surface of water shall make an angle.

  Select all that apply

  • Option A

    tan⁻¹(a/g), tilted backward

  • Option B

    tan⁻¹(a/g), tilted forward

  • Option C

    cot⁻¹(g/a), tilted backward

  • Option D

    cot⁻¹(g/a), tilted forward

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• MCQeasyFluid MechanicsPressure Variation in Fluids

  Three open vessels of different shapes have equal base areas and contain the same liquid up to the same vertical height. Which statement about the pressure at the centre of the base of each vessel is correct?

  Options

  • Option A

    The pressure is greatest in the vessel containing the largest volume of liquid.

  • Option B

    The pressure is greatest in the vessel whose side walls diverge outward.

  • Option C

    The pressure is the same in all three vessels.

  • Option D

    The pressure is proportional to the total weight of liquid present in each vessel.

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• MCQmediumFluid MechanicsPressure Variation in Fluids

  A sealed rectangular tank of length L is completely filled with a liquid of density ρ and accelerates horizontally with acceleration a. The pressure difference between the rear and front vertical walls at the same height is:

  Options

  • Option A

    ρaL

  • Option B

    ρgL

  • Option C

    ρL√(g²+a²)

  • Option D

    Zero

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• MCQmediumFluid MechanicsPressure Variation in Fluids

  A U-tube is rotated about one vertical limb with angular speed ω. The horizontal separation of the limbs is L and tube diameter is negligible compared with L. Find the difference H between the liquid levels.

  

  Options

  • Option A

    L²ω²/(2g)

  • Option B

    Lω²/(2g)

  • Option C

    L²ω/g

  • Option D

    2L²ω²/g

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• Multi-correctmediumFluid MechanicsPressure Variation in Fluids

  A liquid is at rest in a container rotating with constant angular speed ω about a vertical axis. Which statements are correct?

  Select all that apply

  • Option A

    The free surface is a paraboloid

  • Option B

    At the same height, pressure increases with radial distance from the axis

  • Option C

    The height difference between radii r₁ and r₂ is ω²(r₂²-r₁²)/(2g)

  • Option D

    Pressure is independent of radial coordinate at a fixed height

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• NumericeasyFluid MechanicsPressure Variation in Fluids

  A vessel accelerates upward with acceleration 2g. If a vertical liquid column of height h has pressure difference ΔP=nρgh between its bottom and top, find n.

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• MCQmediumFluid MechanicsPressure Variation in Fluids

  A U-tube of uniform cross-section contains a liquid and is accelerated horizontally with acceleration a. The horizontal separation between the two vertical arms is l. The difference in liquid levels is:

  Options

  • Option A

    al/g

  • Option B

    gl/a

  • Option C

    a²l/g²

  • Option D

    l√(g²+a²)/g

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• Multi-correctmediumFluid MechanicsPressure Variation in Fluids

  Neglect capillary effects. Which of the following statements about ideal manometers and barometers are correct?

  Select all that apply

  • Option A

    The vertical height of an ideal barometric column is independent of the tube cross-sectional area.

  • Option B

    Tilting a barometer changes the length of the liquid column but not its vertical height for unchanged atmospheric pressure.

  • Option C

    A barometer in an upward-accelerating elevator shows a smaller vertical column height if atmospheric pressure remains unchanged.

  • Option D

    In a stationary U-tube containing one liquid and open to the same atmosphere at both ends, the two free surfaces are at the same horizontal level.

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• MCQmediumFluid MechanicsPressure Variation in Fluids

  An air bubble of volume 1 cm³ rises from the bottom of a lake 40 m deep to the surface at a temperature of 12°C. The atmospheric pressure is 1 × 10⁵ Pa, the density of water is 1000 kg/m³ and g = 10 m s⁻². There is no difference of the temperature of water at the depth of 40 m and on the surface. The volume of air bubble when it reaches the surface will be:

  Options

  • Option A

    3 cm³

  • Option B

    4 cm³

  • Option C

    2 cm³

  • Option D

    5 cm³

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