GATE Papers >> Mechanical >> 2019 >> Question No 56

Question No. 56 Mechanical | GATE 2019

A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m3 . Liquid of density 1000 kg/m3 is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is ______ mm.

Answer : 80 to 80

Solution of Question No 56 of GATE 2019 Mechanical Paper

$ \begin{array}{l}\mathrm W={\mathrm F}_{\mathrm B}\\{\mathrm\rho}_{\mathrm b}\;{\mathrm V}_{\mathrm b}\mathrm g={\mathrm\rho}_{\mathrm L}\;{\mathrm V}_{\mathrm d}\mathrm g\\{\mathrm\rho}_{\mathrm b}\times\mathrm A\times\left(100\mathrm{mm}\right)\times\mathrm g={\mathrm\rho}_{\mathrm L}{\left(\mathrm A\times\mathrm h\right)}_{\mathrm g}\\\mathrm h=\left(\frac{{\mathrm\rho}_{\mathrm b}}{{\mathrm\rho}_{\mathrm L}}\right)\times100\mathrm{mm}=80\mathrm{mm}\end{array} $   

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