First slide

Fluid statics

Question

A container is partially filled by water. A cork ball is tied to the bottom of the vessel by a string and the ball is completely submerged in water as shown in figure. The string is now cut. Then level of water in the vessel

Moderate

A

falls
B

rises
C

remains unchanged
D

may rise or fall depending upon the size of the ball.

Solution

After the string is cut, the ball will rise to the surface of water and float in water. If V be the volume of the ball and v' be the volume displaced by the ball when floating, then by Law of floatation,
$V^{1} ρg = Vσg \Rightarrow V^{1} = (\frac{σ}{ρ}) V$
Since $σ$ (density of ball) $< ρ$ (density of water), $V^{1} < V$ .
Therefore the level of water falls.

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