Question

Anushka noted down the following observations in her practical book.
$i.$ Weight of the metal block in air $=260$ $g-wt$
$ii.$ Weight of the metal block in water $=220$ $g-wt$
$iii.$ Weight of the metal block in salt water $=180$ $g-wt$
Find the relative density of the salty water.

Answer 1

Weight of metals block in air $=260$ $g$

Weight of metal block in water $=220$ $g$

$w_1=v\rho g$

$v=$ Volume of metal block

$\rho =$ Density of metal

$\sigma =$ Density of water $\left(1gm/c{m}^3\right)$

$w_1=260$ $g=V\times \rho \times 9.8$

$w_2=220$ $g=V\times 1\times 9.8$

$\Rightarrow \frac{w_2}{w_1}=\frac{220}{260}=\frac{V\times 1\times 9.8}{V\times \rho \times 9.8}$

$\Rightarrow \rho =\frac{260}{220}=1.18$

Now,

Weight of metal block in salt water $=180$ $g=w_3$

$a=$ Density of salty water

$\Rightarrow \frac{w_3}{w_1}=\frac{V\times a\times 9.8}{V\times 1.18\times 9.8}=\frac{180}{260}$