Question

An oil of relative density $1.2$ and volume $1\mathrm{litre}$ is poured in water. Find the mass of the oil.

Answer 1

Step 1: Given data

Volume of oil, $V=1\mathrm{litre}=1000{\mathrm{cm}}^3$

Relative density of oil, $\mathrm{R}.\mathrm{D}.=1.2$

Step 2: Calculating the density of oil

Relative density $(\mathrm{R}.\mathrm{D}.)$of a substance is the density of the substance ($d_{subs\tan ce}$) with respect to the density of water ($d_{water}$). It is given by:

$\mathrm{R}.\mathrm{D}.=\frac{d_{subs\tan ce}}{d_{water}}$

The density of water is $1\mathrm{g}/{\mathrm{cm}}^3$

For the oil, the density will be

$$\begin{gathered} \mathrm{R}.\mathrm{D}.=\frac{d_{oil}}{d_{water}} \\ 1.2=\frac{d_{oil}}{1\mathrm{g}/{\mathrm{cm}}^3} \\ {d}_{oil}=1.2\mathrm{g}/{\mathrm{cm}}^3 \end{gathered}$$

Step 3: Calculating the mass of oil

The density of a substance of mass $m$ having volume $V$ is given by:

$d=\frac{m}{V}$

Substituting the values of density and volume of oil, the mass of the oil is calculated as:

$$\begin{gathered} 1.2=\frac{m}{1000} \\ m=1200\mathrm{g} \\ =1.2\mathrm{kg} \end{gathered}$$

Thus, the mass of the oil is $1.2\mathrm{kg}$