Pascal's Law, Buoyant Force and Archimedes' Principle questions with solutions

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• Multi-correctmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  Which statements about floating ice and objects embedded in ice are correct under ideal conditions?

  Select all that apply

  • Option A

    Pure ice floating in pure water does not change the water level after melting.

  • Option B

    If a dense iron piece is embedded in floating ice and sinks after the ice melts, the final water level is lower.

  • Option C

    If a light cork piece is embedded in floating ice and remains floating after the ice melts, the final water level remains unchanged.

  • Option D

    Ice floating in a liquid denser than water can produce a rise in liquid level after melting into water, if mixing-volume change is neglected.

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• MCQmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A dumbbell has spherical ends of masses M and 2M, each volume V, connected by a light rod. In water of density ρ, adding a mass m at the shown point makes both spheres exactly half submerged and the rod horizontal. Find the geometric ratio asked in the figure.

  

  Options

  • Option A

    d(Vρ-3M)/[2(Vρ-2M)]

  • Option B

    d(Vρ-2M)/[2(Vρ-3M)]

  • Option C

    d(Vρ+2M)/[2(Vρ-3M)]

  • Option D

    d(Vρ-2M)/[2(Vρ+3M)]

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• MCQmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A cone of radius R and height H is hanging inside a liquid of density ρ by means of a string as shown in this figure. The force, due to the liquid acting on the slant surface of the cone is (Neglect atmosphere pressure) ρ.

  

  Options

  • Option A

    ρπgH$R^2$

  • Option B

    πρH$R^2$

  • Option C

    πρgH$R^2$

  • Option D

    $\frac23$πρgH$R^2$

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• Multi-correctmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A solid sphere of density ρ_s is completely immersed in a liquid of density ρ_l and released from rest, neglecting drag. Which statements are correct?

  Select all that apply

  • Option A

    If ρ_s<ρ_l, initial acceleration is upward

  • Option B

    Its acceleration magnitude is g|ρ_l-ρ_s|/ρ_s

  • Option C

    For ρ_s=ρ_l it remains in neutral equilibrium

  • Option D

    Buoyant force depends on depth in an incompressible liquid

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• MCQmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying the load is 250 cm². The maximum pressure the smaller piston would have to bear is [Assume g = 10 m s⁻²]:

  Options

  • Option A

    2 × 10⁵ Pa

  • Option B

    20 × 10⁶ Pa

  • Option C

    200 × 10⁶ Pa

  • Option D

    2 × 10⁶ Pa

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• MCQmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  Two cylindrical vessels of equal cross-sectional area 2 m² contain water up to heights 10 m and 6 m respectively. They are connected at the bottom. Take water density 1000 kg/m³ and g = 10 m/s². The work done by gravity is:

  Options

  • Option A

    4×10⁴ J

  • Option B

    8×10⁴ J

  • Option C

    1×10⁵ J

  • Option D

    6×10⁴ J

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• MCQmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  The tension in a string holding a solid block below the surface of a liquid (whose density is greater than the block density) is T₀ when the system is at rest. What is the string tension if the whole system accelerates upward with acceleration a?

  

  Options

  • Option A

    T₀(1 + a/g)

  • Option B

    T₀(1 - a/g)

  • Option C

    2T₀(1 - a/g)

  • Option D

    3T₀(1 + 2a/g)

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• MCQmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A large vessel contains two immiscible liquids of densities d and 2d, each of height H/2. A homogeneous solid cylinder of length L < H/2 and cross-sectional area A/5 floats vertically across the liquid-liquid interface, with L/4 in the denser liquid. Find the density of the cylinder.

  

  Options

  • Option A

    5d/4

  • Option B

    3d/4

  • Option C

    d

  • Option D

    3d/2

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• MCQmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil is: (specific gravity of kerosene oil = 0.8, specific gravity of ice = 0.9)

  

  Options

  • Option A

    8 : 9

  • Option B

    5 : 4

  • Option C

    9 : 10

  • Option D

    1 : 1

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• MCQeasyFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A hydraulic machine has piston areas A and 16A. The small piston is moved down with constant speed v. Neglect compressibility and losses. The speed of the large piston is:

  Options

  • Option A

    v/16

  • Option B

    v/4

  • Option C

    4v

  • Option D

    16v

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