A raft of wood (density 600 kg/${\mathrm{m}}^3$) of mass 150 kg floats in water. How much weight can be put on the raft to make it just sink?

Volume of raft = V = $\frac{\mathrm{mass}}{\mathrm{density}}$

V = $\frac{150}{600} = \frac{1}{4}{\mathrm{m}}^3$

When the raft is totally immersed in water, it displaces $\frac{1}{4}{\mathrm{m}}^3$ water. so the upthrust.

= $\frac{1}{4}\times 1000\times \mathrm{g} \mathrm{newton}$

If x kg is the extra weight put on the raft to fully immerse it in water, then

(x+150)g = $\frac{1}{4}$ x 1000 x g or = x+150 = 250

x = 100 kg