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GATE 2016 ME (ME2) – Question 49

Fluid Mechanics · Fluid properties, fluid statics, forces on submerged bodies, stability of floating bodies · 2 marks · Numerical answer

The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that 45 percent of its volume is in oil while the rest is in water. The density of the body is _________ kg/m3. The specific gravity of oil is 0.7 and density of water is 1000 kg/m3. Acceleration due to gravity g = 10 m/s2.

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Correct answer: 860 to 870

Explanation

Weight equals the sum of buoyancies from the two displaced fluids. Dividing by gV gives body density0.45·ρoil+0.55·ρwater. Oil density is0.7·1000=700kg/m³, so result is0.45·700+0.55·1000=**865kg/m³**.