GATE 2019 ME (ME1) – Question 56
A cube of side 100 mm and density 800 kg/m³ rests on one face at the bottom of an empty container. Liquid of density 1000 kg/m³ is added. Find minimum liquid height at which the cube just lifts (mm).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 80 to 80
Explanation
At lift-off, buoyancy equals weight: $\rho_l gAh=\rho_c gA(100\ \mathrm{mm})$. Hence $h=(800/1000)(100)=\mathbf{80}$ mm. This official result assumes liquid can reach the underside; perfectly sealed contact with the floor would prevent the assumed upward pressure.