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Q53 (NDA-I/2023) Science & Technology › Basic Science (Physics, Chemistry, Biology) Official Key

A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 <1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then :

Explanation

According to the Law of Floatation, for an object to float, its weight must be balanced by the buoyant force (the weight of the displaced fluid). The equilibrium equation is:

Weight of object = Buoyant Force
(ρs × V × geff) = (ρw × Vsub × geff)

Where ρs is the density of the sphere, ρw is the density of water, and geff is the effective acceleration (gravity on Earth or acceleration a in the spaceship).

  • On Earth: ρs × V × g = ρw × (f1V) × g ⇒ f1 = ρs / ρw
  • On the spaceship: ρs × V × a = ρw × (f2V) × a ⇒ f2 = ρs / ρw

Since the effective acceleration terms cancel out on both sides, the fraction of submerged volume depends strictly on the ratio of the densities. As the densities remain constant, f2 = f1.

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