Question

The block of wood of mass 24 kg floats in water. The volume of the wood is $0.032{\mathrm{m}}^3$. Find

1. The volume of the block below the surface of water.
2. The density of wood.

Answer 1

Step-I: Given

Mass of block of wood=$\mathrm{M}=24\mathrm{kg}$

Volume of the wood=$\mathrm{V}=0.032{\mathrm{m}}^3$

Density of water=${\rho }_{\mathrm{w}}=1000\raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^3$}\right.$

Volume of block below the surface of water =?

Density of wood=?

Step-II: Formula

Density =$\frac{\mathrm{M}}{\mathrm{V}}$

$\frac{\mathrm{Volume}\mathrm{of}\mathrm{block}\mathrm{submerged}\mathrm{in}\mathrm{water}}{\mathrm{Total}\mathrm{volume}\mathrm{of}\mathrm{block}}=\frac{\mathrm{Density}\mathrm{of}\mathrm{the}\mathrm{body}}{\mathrm{Density}\mathrm{of}\mathrm{water}}$

Step-III: Calculation

1.Calculate the density of the block of wood

Density =$\frac{\mathrm{M}}{\mathrm{V}}=\frac{24}{0.032}=\frac{2400}{32}=\frac{300}{4}=750\raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^3$}\right.$

2.Calculate Volume of block below the surface of water

$\frac{\mathrm{Volume}\mathrm{of}\mathrm{block}\mathrm{submerged}\mathrm{in}\mathrm{water}}{\mathrm{Total}\mathrm{volume}\mathrm{of}\mathrm{block}}=\frac{\mathrm{Density}\mathrm{of}\mathrm{the}\mathrm{body}}{\mathrm{Density}\mathrm{of}\mathrm{water}}$

$\frac{\mathrm{\nu }}{\mathrm{V}}=\frac{{\mathrm{d}}_{\mathrm{wood}}}{{\mathrm{d}}_{\mathrm{water}}}$

$\mathrm{\nu }=\frac{{\mathrm{d}}_{\mathrm{wood}}\times \mathrm{V}}{{\mathrm{d}}_{\mathrm{water}}}=\frac{750\times 0.032}{1000}=0.024{\mathrm{m}}^3$