91Ó°ÊÓ

The given data is listed below as-

• The dimensions of the wooden block are, $20 \mathrm{cm}×10 \mathrm{cm}×6 \mathrm{cm}$
• The density of the wood is,${\mathrm{ÒÏ}}_{wood}=0.7 \frac{\mathrm{g}}{{\mathrm{cm}}^3}$
• The density of water is, ${\mathrm{ÒÏ}}_{water}=1 \frac{\mathrm{g}}{{\mathrm{cm}}^3}$

The displacement of water occurs when a wooden block floats on water. The mass of the water is equal to the displacement of water.

The concept of the displacement of water gives the depth of block.

The equation of mass of the block is given by displacement of the water

The density is given by-

$$\begin{gathered} \mathrm{ÒÏ}=\frac{mass}{Volume} \\ mass=\mathrm{ÒÏ}×Volume \end{gathered}$$

Now, mass of water= mass of wood

$$\begin{gathered} m_{water}=m_{wood} \\ ={\mathrm{ÒÏ}}_{wood}.V_{wood} \end{gathered}$$

For ${\mathrm{ÒÏ}}_{wood}=0.7\frac{g}{c{m}^3}$and

$$\begin{gathered} V_{wood}=0.20×0.10×0.06 \\ =0.0012{\mathrm{m}}^3 \\ {m}_{wood}=0.7×{10}^3\left(\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right)×0.0012\left({\mathrm{m}}^3\right) \\ =0.84\mathrm{kg} \end{gathered}$$

Now, find the volume of water by density of water

role="math" localid="1658901709608" $$\begin{gathered} V_{water}=\frac{m_{water}}{{\mathrm{ÒÏ}}_{water}} \\ =\frac{0.84kg}{1×{10}^3{\displaystyle \frac{kg}{m^3}}} \\ =0.84×{10}^{-3}{\mathrm{m}}^3 \end{gathered}$$

The displaced water takes the shape of the cube same as the shape of a block with an area,

$A=0.20×0.10×h$

The height is the depth of the block which is given by:

$$\begin{gathered} h=\frac{V_{water}}{A} \\ =\frac{0.84×{10}^{-3}}{0.20×0.10m} \\ =0.042\mathrm{m} \\ =4.2\mathrm{cm} \end{gathered}$$

Thus, the block is 4.2 cm below the surface of water .