Question
When a 200 gm piece of metal is weighed in pure water, its weight is 160 gm. Find the relative density of the metal and the volume of the piece.
✓
Answer
Relative density of metal
$\begin{array}{l}=\frac{\text { Weight of metal in air }}{\begin{array}{c}\text { Reduction in weight when } \\\text { weighed in water }\end{array}} \\=\frac{200}{200-160}=\frac{200}{40}=5\end{array}$
Density of metal $=$ Relative density of metal $\times$ density of water
$=5 \times 1=5 gm / cm^3$
$\therefore$ Volume of piece $=\frac{\text { Mass }}{\text { Density }}=\frac{200 gm }{5 gm / cm ^3}$
$\begin{array}{l}=\frac{\text { Weight of metal in air }}{\begin{array}{c}\text { Reduction in weight when } \\\text { weighed in water }\end{array}} \\=\frac{200}{200-160}=\frac{200}{40}=5\end{array}$
Density of metal $=$ Relative density of metal $\times$ density of water
$=5 \times 1=5 gm / cm^3$
$\therefore$ Volume of piece $=\frac{\text { Mass }}{\text { Density }}=\frac{200 gm }{5 gm / cm ^3}$
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