Question
Download Solution PDFA metallic body floats at the interface of mercury of specific gravity of 13.6 and water such that 40% of its volume is submerged in mercury and 60% in water. The density (kg/m3) of the metallic body is approximately __________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:-
Archimedes' Principle -
When an object is submerged in a fluid, it experiences a buoyant force, B. This buoyant force results from the pressure-based forces on the surfaces of the submerged object.
Archimedes’ Principle states that the magnitude of the buoyant force is equal to the weight of the fluid displaced by the submerged object.
⇒ B = Wdisplaced-fluid = mdisplaced-fluid × g = ρfluid. Vdisplaced-fluid. g
If the object is completely submerged in the fluid, the volume of displaced fluid equals the volume of the submerged object:
Vdisplaced-fluid = Vobject.
Calculation:-
Given:-
ρHg = Density of mercury = 13.6 × 1000 = 13600 kg/m3 ....(As the density of water = 1000 kg/m3)
ρwater = 1000 kg/m3
40% of the volume of the object is submerged in mercury and 60% in water.
Let, V = Volume of the object
ρobject = ?
As we know from the Archimedes principle, the buoyancy force is equal to the weight of the fluid displaced by the submerged object.
As the body fully submerges in fluids, the buoyancy force equals the object's weight.
Object's weight = ρobject. V. g ...(1)
Buoyancy force,
B = ρfluid. Vdisplaced-fluid. g
B = (13600 × 0.4V + 1000 × 0.6V)g ...(2)
On putting equation (1) equals to equation (2),
ρobject. V. g = (13600×0.4V + 1000×0.6V)g
⇒ ρobject = 6040 kg/m3
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