The density and mass of a metal block are 3.2 ×10^{3} kg m^{-3} and 5.0 kg respectively. Find the upthrust that act on the metal block when it is fully immersed in water. [ Density of water = 1000kg m^{-3} ]

**Answer**

The upthrust can be found from the formula F = ρVg.
From the question, we know that

Density of the water, ρ
= 1000kg m^{-3}

Gravitational field strength, g = 10 ms^{-2}

Since the metal block is fully immersed in water, the volume of the displaced water = volume of the block.

The volume of the block, V
can be found be using the equation of density, ρ = m/V.

$\begin{gathered}
{\text{Density of Block, }}\rho_{metal} {\text{ = 3200kgm}}^{{\text{ - 3}}} \hfill \\
{\text{Mass of Block, }}m = 5kg \hfill \\
{\text{Hence, Volume of Block,}} \hfill \\
V = \frac{m}
{\rho } = \frac{{(5)}}
{{(3200)}} = 0.0015625m^3 \hfill \\
\end{gathered} $

Upthrust exerted on the block,

$\begin{gathered}
F = \rho Vg \hfill \\
F = (1000)(0.0015625)(10) \hfill \\
F = 14.625N \hfill \\
\end{gathered} $