An empty cylindrical container, open at the top is floating in water with its axis vertical with 50% of its volume submerged in water. Wall of the container is very thin. Now water is poured in the cylinder so as to fill 25% of its volume. What fraction of the volume of the container will be submerged in water now?
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a
0.55
b
0.65
c
0.75
d
0.85
answer is C.
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Detailed Solution
If m be the mass of container, V be its volume and ρ be the density of water, then initially, mg=V2ρ.gAfter water is poured in the container let volume submerged in water be V1.∴ ρV1g=mg+V4ρ.g⇒ρV1g=V2ρg+V4ρg⇒V1V=34=0.75