Project ForgeFluid Mechanics
Fluid Statics
GATE 2019
Medium
A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the cube's material is 800 kg/m³. Liquid of density 1000 kg/m³ is poured into the container. The minimum height to which the liquid needs to be poured for the cube to just lift up is ___ mm.
80 mm(± 0.5 accepted)
Explanation
The cube lifts off when the buoyant force equals its weight. For liquid height h (h≤100mm), submerged volume = A·h where A is the base area. Setting ρ_liquid·A·h = ρ_cube·A·(100mm): h = (ρ_cube/ρ_liquid)×100 = (800/1000)×100 = 80 mm.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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