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Archimedes' Principle

A wooden cyli...

Question

A wooden cylinder of base area $50 c m^{2}$ and height $1 m$ has mass of $2.5 k g$ . It is carefully lowered in a cylindrical vessel of water. The vessel has inner area $100 c m^{2}$ and height of $1 m$ . Which of the four figures correctly represents the equilibrium state?

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Solution

The correct option is B

For floating, the weight must be balanced by the buoyant force
$m g = B$
$m g = ρ_{w} V_{d} g$
where $ρ_{w}$ is the density of the water and $V_{d}$ is the volume of the water displaced.
$2.5 g = 10^{3} \times 50 \times 10^{- 4} \times h \times g$
$h = \frac{1}{2} m$
volume of water to be displaced for floating $= 50 \times 10^{- 4} \times \frac{1}{2}$
$= 25 \times 10^{- 4} m^{3}$
Actual volume in the container
$V_{i} = 0.2 \times 100 \times 10^{- 4} = 20 \times 10^{- 4} m^{3}$
$V_{i} < V_{d} \to$ so it will not float.

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A wooden cylinder of base area 50 cm2 and height 1 m has mass of 2.5 kg. It is carefully lowered in a cylindrical vessel of water. The vessel has inner area 100 cm2 and height of 1 m. Which of the four figures correctly represents the equilibrium state?

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