$A$ hydraulic lift is shown in the figure. The radii of the movable pistons $P_1$ and $P_2$ are $2 \ m$ and $5 \ m$ respectively. If a block of mass $x$ is placed on $P_2$,then the minimum mass that should be kept on $P_1$ to lift the block on $P_2$ is (in $x$)

In a car lift,compressed air exerts a force $F_{1}$ on a small piston having a radius of $5.0 \; cm$. This pressure is transmitted to a second piston of radius $15 \; cm$. If the mass of the car to be lifted is $1350 \; kg$,calculate $F_{1}$. What is the pressure necessary to accomplish this task? $(g = 9.8 \; m s^{-2})$

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?

$A$ 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

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 heights $h$ in the level of water in the two tubes is ........ $cm$.

Air is blown through a hole on a closed pipe containing liquid. Then the pressure will