The movable cylindrical pistons $P_1$ and $P_2$ of a hydraulic lift are of radii $2 \,m$ and $R$ respectively. $A$ body of mass $32 \,kg$ on piston $P_2$ is supported by a body of mass $2 \,kg$ placed on piston $P_1$. The value of $R$ is (in $\,m$)

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?

In a hydraulic lift,if the radius of the smaller piston is $5 \ cm$,and the radius of the larger piston is $50 \ cm$,then the weight that the larger piston can support when a force of $250 \ N$ is applied to the smaller piston is (in $kN$)

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 $\text{ N}$)

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?

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? $(g = 9.8 \; m s^{-2})$