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  4. A wooden cube just floats inside water with a 200 gm mass placed on it. When the mass is removed, the cube floats with its top surface 2 cm above the water level. What is the side of the cube?

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Q. A wooden cube just floats inside water with a $200\, gm$ mass placed on it. When the mass is removed, the cube floats with its top surface $2\, cm$ above the water level. What is the side of the cube?

Mechanical Properties of Fluids

Solution:

Mass $\times g=$ Volume of part of cube $\times \rho \times g$
$\Rightarrow 200 \times g=L^{2}\left(2 \times \rho_{w} \times g\right)$
$\Rightarrow 100=L^{2} \left\{\because \rho_{w}=1\right\}$
$\Rightarrow 10\, cm =L$
From the two figures we can see that the $200\, gm$ block is provided with required buoyant force but a part of cube which is afloat in $2^{\text {nd }}$ figure.
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