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Question

When a cube of wood floats in water, 60% of its volume is submerged. When the same cube floats in an unknown fluid, 85% of its volume is submerged. Then:

A
Density of wood is 500 kg/m3
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B
Density of wood is 600 kg/m3
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C
Density of the unknown fluid is 800 kg/m3
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D
Density of the unkonwn fluid is 706 kg/m3
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Solution

The correct option is D Density of the unkonwn fluid is 706 kg/m3
Let the volume of the cube be V.


When wooden cube is submerged in water:
Applying equilibrium condition along vertical direction,
Fbwmg=0
ρwgVf=ρbVg ...(i)
[Vfvolume of displaced fluid]
& Vf=0.60×V
Hence from Eq.(i),
1000×(0.6V)=ρbV
ρb=600 kg/m3 ...(ii)

When wooden cube is submerged in unknown fluid:
Applying equilbrium condition along vertical direction,
Fbfmg=0
ρfgVf=ρbVg
[Vfvolume of displaced fluid]
& Vf=0.85×V and substituting from Eq.(ii),
ρf×0.85V=600×V
ρf706 kg/m3
Hence, options (b) & (d) are correct.

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