First slide

Fluid statics

Question

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?

Easy

A

0.55
B

0.65
C

0.75
D

0.85

Solution

If m be the mass of container, V be its volume and $ρ$ be the density of water, then initially, $m g = \frac{V}{2} ρ . g$
After water is poured in the container let volume submerged in water be $V^{1}$ .
$∴ ρ V^{1} g = m g + \frac{V}{4} ρ . g$
$\Rightarrow ρ V^{1} g = \frac{V}{2} ρ g + \frac{V}{4} ρ g \Rightarrow \frac{V^{1}}{V} = \frac{3}{4} = 0.75$

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