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?

$A$ hydraulic automobile lift is designed to lift cars with a maximum mass of $3000 \, kg$. The area of cross-section of the piston carrying the load is $425 \, cm^{2}$. What is the maximum pressure the smaller piston would have to bear?

Two syringes of different cross-sections (without needles) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are $1.0 \; cm$ and $3.0 \; cm$ respectively.
$(a)$ Find the force exerted on the larger piston when a force of $10 \; N$ is applied to the smaller piston.
$(b)$ If the smaller piston is pushed in through $6.0 \; cm$,how much does the larger piston move out?

Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This law was first formulated by

$A$ hydraulic press containing water has two arms with diameters as shown in the figure. $A$ force of $10 \,N$ is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is . . . . . . $N$.

The area of cross-section of the wider tube shown in the figure is $800\,cm^2$. If a mass of $12\,kg$ is placed on the massless piston,the difference in the heights $h$ in the level of water in the two tubes is ........ $m$.