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Question

Two cubical blocks identical in dimensions float in water in such a way that the first block floats with half part immersed in water and the second block floats with 3/4 th of its volume immersed inside the water. The ratio of density of first block to that of second block is

A
2:3
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B
3:4
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C
1:3
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D
1:4
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Solution

The correct option is A 2:3
For floating of block,
Fb=mg
Vfρfg=Vbρ1g ...(i)
Vf volume of fluid displaced
Vbvolume of both blocks
Both blocks will have same volume due to same dimensions.
ρ1 density of first block
According to question, for first block:
Vf=Vb2
From Eq.(i),
12Vbρfg=Vbρ1g
ρf=2ρ1 ...(ii)
And for second block:
Vf=34Vb
From Eq.(i),
34Vbρfg=Vbρ2g
ρf=43ρ2 ...(iii)

From Eq.(ii) & (iii),
2ρ1=43ρ2
ρ1ρ2=23

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