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Two metallic balls when completely immersed in water have equal upthrust on them, then which statement is correct: a) Both balls must have equal weights b) Both balls must have equal densities c) Both balls must have an equal volume

Two metallic balls when completely immersed in water have equal upthrust on them, then which statement is correct: a) Both balls must have equal weights b) Both balls must have equal densities c) Both balls must have an equal volume Correct Answer Only c is correct

CONCEPT:

Archimedes Principle:

  • 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.

EXPLANATION:

  • The upthrust on the body is independent of the density and the weight of the body.
  • 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.
  • Since the upthrust on both the balls is equal, so the weight of water displaced by both the balls will also be equal,
  • The weight of water displaced is given as,

⇒ W = ρVg     -----(1)

Where ρ = density of water, V = volume of water displaced, and g = gravitational acceleration

  • By equation 1 it is clear that the volume of water displaced will also be equal for both the balls because the upthrust on both the balls is equal.
  • Both the balls are completely immersed in water, so the volume of water displaced by both the balls will be equal to the volume of the balls.
  • Therefore the volume of both the balls will be equal.
  • Hence, option 3 is correct.

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