The diameters of two pistons of a hydraulic press are $0.1\, m$ and $0.6\, m$ respectively. What is the mechanical advantage of the hydraulic press,assuming the effort is applied directly on the pump plunger?

Which law states that the effect of pressure is the same for all portions of a confined fluid?

State and prove Pascal's law.

$A$ hydraulic lift as shown in the figure is used to lift a mass of $1000 \ kg$, which is placed on a piston $(P_1)$ of area $1 \ m^2$. If the cross-section area of the piston $(P_2)$ at the other end is $0.01 \ m^2$, then how much mass needs to be put on it to lift the $1000 \ kg$ (in $kg$)?

In a vehicle lifter, the enclosed gas exerts a force $F$ on a small piston of $8 \text{ cm}$ diameter. The pressure is transmitted to a second piston of diameter $24 \text{ cm}$. If the mass of the vehicle to be lifted is $1400 \text{ kg}$, then $F$ must at least be $(g=10 \text{ ms}^{-2})$. (in $\text{ N}$)

$A$ tall tank filled with water has an irregular shape as shown. The wall $CD$ makes an angle of $45^{\circ}$ with the horizontal,the wall $AB$ is normal to the base $BC$. The lengths $AB$ and $CD$ are much smaller than the height $h$ of water (figure not to scale). Let $p_1, p_2$ and $p_3$ be the pressures exerted by the water on the wall $AB$,base $BC$ and the wall $CD$ respectively. Density of water is $\rho$ and $g$ is acceleration due to gravity. Then,approximately