Question

The volume of 50 g of a substance is $20c{m}^3$. If the density of water is $1gc{m}^{-3}$, will the substance float or sink?

Answer 1

Step 1: Given data

Mass of a substance (m) = 50 g.

The volume of the substance (V) = $20c{m}^3$.

Step 2: Formula used

We know the formula of density,

$Densityofsubs\tan ce=\frac{massofsubs\tan ce}{volumeofsubs\tan ce}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{\left(}\mathit{a}\mathbf{\right)}$

We know that relative density is the ratio of the density of the substance to the density of water at $4°C$

$Relativedensityofsubs\tan ce=\frac{Densityofasubs\tan ce}{Densityofwater}.........\left(b\right)$

Step 3: Calculating the density of a substance

On, putting the given values in equation (a), we get,

$$\begin{gathered} Densityofsubs\tan ce=\frac{50g}{20c{m}^3} \\ Densityofsubs\tan ce=2.5g/c{m}^3. \end{gathered}$$

Step 4: Calculating the relative density of the substance

On, putting all the given values in equation (b)

$$\begin{gathered} Relativedensityofsubs\tan ce=\frac{2.5g/c{m}^3}{1g/c{m}^3} \\ Relativedenistyofsubs\tan ce=2.5 \end{gathered}$$

Note:

1. If the relative density of the substance is more than 1, then the substance will sink into the water.
2. If the relative density of the substance is smaller than 1, then the substance will float in the water.

Hence, the relative density of the substance is 2.5 which is more than 1, the substance will sink into the water.