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Question

A block of wood floats in water (4/5)th of its volume submerged. If the same block just floats in a liquid, the density of liquid in kg/m3 is
(Take density of water as 1000 kg/m3)

A
900 kg/m3
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B
400 kg/m3
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C
1250 kg/m3
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D
800 kg/m3
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Solution

The correct option is D 800 kg/m3
Let V be the volume of the block.
Let density of block and liquid is ρb and ρl
When block floats in water, weight of the block will be equal to the weight of displaced water
ρbVg=(4/5V)ρg
ρb=4/5ρ......(1)
When block is just float in the liquid, weight of the block will be equal to the weight of displaced liquid
ρbVg=ρlVg
ρb=ρl.......(2)
From equation (1) and (2),
ρl=4/5ρ
Density of water (ρ)=1000 kg/m3
ρl=800 kg/m3

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