Question

Anushka noted down the following observations in her notebook,
i) weight of the metal block in air =$260{\rm{ g wt}}$
ii) weight of the metal block in water =$220{\rm{ g wt}}$
iii) weight of the metal block in salt water =$180{\rm{ g wt}}$
Find the relative density of the salty water.

Answer 1

Hint: First, the volume of the metal block in water has to be calculated from the given weights.
Since we know that, density is equal to mass/volume of a substance hence once volume is known
then densities can be determined.
Let ρ, ρ w and ρ sw are the densities of block, water and salty water respectively.
Given,
Weight of the metal block in air =$260{\rm{ g wt}}$
Weight of the metal block in water =$220{\rm{ g wt}}$
Weight of the metal block in salt water =$180{\rm{ g wt}}$
Density of water is, ρ w =1
The volume of the block is v
We know that,
${\rm{Density}}\left( \rho \right) = \dfrac{{{\rm{mass}}\left( m
\right)}}{{{\rm{volume}}\left( v \right)}}$ ……(1)
Therefore, volume of the block is,
$\begin{array}{l}v\rho g = 260g\\ \Rightarrow v\rho = 260\end{array}$
……(2)
Reduced weight of the block= weight of the block -weight of water displaced by block.

$\begin{array}{l}220g = v\rho g - v{\rho _w}g\\ \Rightarrow 220 = v{\rho _{}} - v \times 1\\
\Rightarrow 220 = 260 - v\\ \Rightarrow v = 40c{m^3}\end{array}$
…….(3)
Now,
Reduced weight of the block=weight of the block-weight of the salty water displaced by the
block.
$\begin{array}{l}180g = v\rho g - v{\rho _{sw}}g\\\end{array}$ …….(3)
Substituting the value of $v$ as $40c{m^3}$in equation (3) we get,

$\begin{array}{l} \Rightarrow 180 = v\rho - v{\rho _{sw}}\\ \Rightarrow 180 = 260 - 40{\rho
_{sw}}\\ \Rightarrow {\rho _{sw}} = 2{\rm{ g/c}}{{\rm{m}}^3}\end{array}$
Hence the density of the salty water is obtained as$2{\rm{ g/c}}{{\rm{m}}^3}$.
Note: The students have to apply the formula of calculating densities from mass and volume.
The volume of the block can be calculated from the given weights of the block in water as the density of water is known. Once the volume is obtained, the density of the salty water can be
found as we know that density is mass/volume.