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:
[amp_mcq option1="f₂=f₁" option2="f₂ = (a/g) * f₁" option3="f₂ > f₁” option4=”f₂ = (g/(g-a)) * f₁” correct=”option1″]
This question was previously asked in
UPSC NDA-1 – 2023
The fraction of volume submerged when an object floats in a fluid is determined by the ratio of the object’s density to the fluid’s density ($f = \rho_{object} / \rho_{fluid}$). This relationship arises from the condition that the buoyant force equals the weight of the object. Both the buoyant force (which depends on the effective acceleration) and the weight (which also depends on the effective acceleration) are directly proportional to the effective acceleration. Therefore, the ratio of densities, and hence the fraction of submerged volume, is independent of the magnitude of the uniform effective acceleration (like gravity) acting on the system.