A raft of wood of density 600 $kg{m}^{-3}$  and mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?

Volume of raft $=\frac{120}{600}=\frac{1}{5}{m}^3$ 

Fraction of volume inside water is

$\frac{{\rho }_{wood}}{{\rho }_{water}}=\text{Relative density = }\frac{600}{1000}=\frac{3}{5}$

So, fraction of volume outside water is

$\left(1-\frac{3}{5}\right)=\frac{2}{5}$

$\Rightarrow$  volume outside water is

$V_{out}=\frac{2}{5}\times \frac{1}{5}=\frac{2}{25}{m}^3$

When the body just sinks, the additional upthrust is

$U=\frac{2}{25}\times {10}^3\times g$

If the weight put on the raft is m then

$mg=\frac{2}{25}\times {10}^3\times 10$

$\Rightarrow$  $m=80kg$

$$\begin{gathered} \mathit{I}\mathit{I}\mathbf{ }\mathit{m}\mathit{e}\mathit{t}\mathit{h}\mathit{o}\mathit{d}\mathbf{:} \\ fraction of raft=\frac{120}{600}=\frac{1}{5} \\ Buoyant force=v_i{\rho }_{l}g=\frac{1}{5}\times 1000 kgf=200kgf \\ For floatation, \\ weight =upthrust \\ 120+M=200 \\ M=80kg \end{gathered}$$