Question

A wooden block floats in water with two-third of its volume submerged in water. Calculate the density of the wood.

Answer 1

Step 1: Given data

Let the volume of the block $=V_b$

Volume of the block immersed in water, $V_{bw}=\frac{2}{3}{V}_b$

Density of water, ${\rho }_w=1g/c{m}^3$

Acceleration due to gravity $=g$

Density of block, ${\rho }_b=?$

Step 2: Formula used

$V_b\times {\rho }_b\times g=V_{bw}\times {\rho }_w\times g$ ……………………….(a)

The above equation is strictly in accordance with the law of floatation.

Step 3: Calculation of the density of the block

Substituting the given values in equation (a), we get

$$\begin{gathered} V_b\times {\rho }_b\times g=\frac{2}{3}{V}_b\times 1g/c{m}^3\times g \\ {\rho }_b=\frac{2}{3}\times 1 \\ {\rho }_b=0.66g/c{m}^3 \end{gathered}$$

Hence, the density of the block is equal to 0.66 g/cm³.