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Question

A block of wood floats in water with 45th of its volume submerged but in another liquid, it floats fully submerged. The density of the unknown liquid is (in kg/m3)

A
750
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B
800
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C
1000
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D
1250
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Solution

The correct option is B 800
In first case:
Volume of fluid displaced when block is floating in water,
V=45Vb
where Vb is the volume of block.
Applying the condition for floatation,
Fb=mg
Vρwg=Vbρbg
45Vb×ρw×g=Vb×ρb×g
Or, ρwρb=54
Substituting the values,
ρb=45×ρw
ρb=45×1000=800 kg/m3 ...(i)
When block is put in an unknown liquid of density ρ, it floats in a fully submerged condition.
Volume of fluid displaced=volume of body
Vf=Vb ...(ii),
Applying condition of floatation:
Vfρg=mg
Or, Vfρg=Vbρbg ...(iii)
From Eq.(i), (ii), (iii),
ρ=ρb=800 kg/m3

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