Using the definitions of pressure and density, demonstrate that $p = \rho g h$, where $p$ represents the pressure caused by the liquid acting on the base of the beaker and $g$ is the acceleration of free fall.
Explain why the relation in (a) does not represent the full pressure on the base of the beaker.
Fig. 4.2 displays how the total pressure within the liquid changes with depth $x$ below the surface. Find the density of the liquid.
A solid cylinder is supported by a wire so that the cylinder’s base is level with the liquid surface, as shown in Fig. 4.3. The cylinder has length $4.0 \times 10^{-2}\,\text{m}$ and cross-sectional area $3.7 \times 10^{-4}\,\text{m}^2$. The tension in the wire is $0.53\,\text{N}$. The cylinder is then lowered and held at rest by the wire so that the top of the cylinder is level with the liquid surface. Calculate the new tension in the wire.