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An object X sinks in liquids P and Q but floats in liquid R. Which of the following conclusions can be made from these observations? A) Density of X is more than the density of P B) Density of X is less than the density of R C) Density of P is equal to the density of R D) Density of P is less than the density of R

An object X sinks in liquids P and Q but floats in liquid R. Which of the following conclusions can be made from these observations? A) Density of X is more than the density of P B) Density of X is less than the density of R C) Density of P is equal to the density of R D) Density of P is less than the density of R Correct Answer A, B, D

Concept:

Archimedes principle:

  •  It states that a body, when wholly or partially immersed in liquid, experiences an upward thrust that is equal to the volume of the liquid.
  • Archimedes Principle is also known as the physical law of buoyancy.
  • When a solid is fully immersed in a liquid, it loses weight, which is equal to the weight of the liquid it displaces.

Apparent weight= actual weight−buoyant force= mg−ρgV

Where m = mass of the object and ρ = density of the fluid

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 Buoyant force:

  • ​When a body is wholly or partially immersed in a fluid at rest, the fluid exerts pressure on the surface of the body in contact with the fluid.
  • The pressure is greater on lower surfaces of the body than on the upper surfaces as the pressure in a fluid increases with depth.
  • The resultant of all the forces is an upward force called buoyant force

Explanation:

Law of Floatation:

  • When an object is placed on liquid, an upthrust acts on it.
  • This upthrust is more than weight when the density of the object is less than weight. The object floats in this case.
  • If the density of the object is more, the object will sink as the weight will be more than upthrust.
  • When a body is immersed partially or completely in a fluid (liquid or gas), it experiences an upthrust or buoyant force that is equal to the weight of the fluid displaced by the body.
  • Considering, the question statement:
    • ρR > ρX > ρP

So, from the above relation options A, B, and D are the correct ones.

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