A cylinder of mass M and average density d₁ is lowered into a vessel of cross-sectional area A, half full of liquid of density ${\mathrm{d}}_2\left({\mathrm{d}}_2<{\mathrm{d}}_1\right.$) until it is completely covered. The increase in pressure at bottom of vessel is

The volume of liquid displaced when the cylinder is immersed
$=\frac{\mathrm{M}}{{\mathrm{d}}_1}$
$\text{ Resultant upward thrust }=\frac{\mathrm{M}}{{\mathrm{d}}_1}\times {\mathrm{d}}_2\mathrm{g}$
$\therefore \text{ Thrust on liquid surface }$
$=\frac{\mathrm{M}}{{\mathrm{d}}_1}\times {\mathrm{d}}_2\mathrm{g}\text{ (Newton's third law) }$
This thrust is experienced by bottom
Increase of pressure at bottom
$=\frac{{\mathrm{Md}}_2\mathrm{g}}{{\mathrm{d}}_1\mathrm{A}}$