First slide

Pressure in a fluid-mechanical properties of fluids

Question

A cubical block of wood of side a and density $ρ$ floats in water of density 2 $ρ$ . The lower surface of the cube just touches the free end of a massless spring of force constant K fixed at the bottom of the vessel. The weight W put over the block so that it is completely immersed in water without wetting the weight is

Moderate

A

$a (a^{2} ρg + K)$
B

$a (aρg + 2 K)$
C

$a (\frac{aρg}{2} + 2 K)$
D

$a (a^{2} ρg + \frac{K}{2})$

Solution

Since density of block = 1/2(density of water), 50% of its volume is immersed in water.
In the second case, half of the volume of the block is further immersed in water.
Therefore, W = Extra upthrust + Spring force
$= a \times a \times \frac{a}{2} \times 2 ρ \times g + K (\frac{a}{2})$
$= a (a^{2} ρg + \frac{K}{2})$

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