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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 800In 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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