Question

The dimensions of the wooden block are $2m\times 0.25m\times 0.10m.$ Calculate the mass of the block. [Given : Relative density of wood = 0.6, density of water = ${10}^{3}kg{m}^{-3}$].

Answer 1

Step 1: Given:

Dimension of block $=2m\times 0.25m\times 0.10m$

Relative density of wood $=0.6$

Density of water = ${10}^{3}kg{m}^{-3}$

Step 2: Calculate the density of wood,

The ratio of a substance's density (mass per unit volume) to the density of water is known as relative density or specific gravity.

$\mathit{R}\mathit{e}\mathit{l}\mathit{a}\mathit{t}\mathit{i}\mathit{v}\mathit{e}\mathbf{}\mathit{d}\mathit{e}\mathit{n}\mathit{s}\mathit{i}\mathit{t}\mathit{y}\mathbf{=}\frac{\mathbf{D}\mathbf{e}\mathbf{n}\mathbf{s}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{w}\mathbf{o}\mathbf{o}\mathbf{d}}{\mathbf{D}\mathbf{e}\mathbf{n}\mathbf{s}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{w}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{r}}$

Density of wood$=0.6\times 1000$

$=600kg{m}^{-3}$

Step 3: Calculate the mass,

The density of a substance is defined as its mass per unit volume.

$\mathit{D}\mathit{e}\mathit{n}\mathit{s}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{w}\mathit{o}\mathit{o}\mathit{d}\mathbf{=}\frac{\mathbf{M}\mathbf{a}\mathbf{s}\mathbf{s}}{\mathbf{V}\mathbf{o}\mathbf{l}\mathbf{u}\mathbf{m}\mathbf{e}}$

The volume of the block, $V=2m\times 0.25m\times 0.10m$

$=0.05m^3$

Thus, the mass of block$\mathbf{=}\mathbf{600}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{05}$$\mathbf{=}\mathbf{30}\mathit{k}\mathit{g}$

Hence, the mass of the block is $\mathbf{30}\mathit{k}\mathit{g}$.