A sphere falls from rest into water from a height of 2 m, the relative density of the sphere is 0.80. Find the depth to which ball will sink (in m).

Velocity of the ball when reaches surface of water, $\mathrm{v}=\sqrt{2\mathrm{gh}}=\sqrt{4\mathrm{g}}$
Acceleration inside the water
$\mathrm{a}=\frac{\text{ apparent weight }}{\mathrm{m}}=\frac{\mathrm{mg}\left(1-\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)}{\mathrm{m}}=\mathrm{g}\left(1-\frac{10}{0.8}\right)=-\frac{\mathrm{g}}{4}$
Let say it goes to a depth x, then using ${\mathrm{v}}^2={\mathrm{u}}^2+2\mathrm{as}\Rightarrow 0=4\mathrm{g}-2\times \frac{\mathrm{g}}{4}\times \mathrm{x}\Rightarrow \mathrm{x}=8\mathrm{m}$