$A$ hydraulic press can lift $100\, kg$ when a mass $'m'$ is placed on the smaller piston. It can lift ......... $kg$ when the diameter of the larger piston is increased by $4$ times and that of the smaller piston is decreased by $4$ times,keeping the same mass $'m'$ on the smaller piston.

$A$ 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 maximum pressure would the smaller piston have to bear?

$A$ hydraulic lift is shown in the figure. The radii of the movable pistons $P_1$ and $P_2$ are $2 \,m$ and $8 \,m$ respectively. If a body of mass $2 \,kg$ is placed on piston $P_1$, then the force on piston $P_2$ is (Ignore atmospheric pressure, acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,N$)

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 $\text{ N}$)

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?

$A$ hydraulic lift is shown in the figure. The movable pistons $A, B$ and $C$ have radii of $10 \,cm, 100 \,cm$ and $5 \,cm$ respectively. If a body of mass $2 \,kg$ is placed on piston $A$, what are the maximum masses that can be lifted by pistons $B$ and $C$ respectively?