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 $\text{ N}$)

$A$ piston of cross-section area $100 \, cm^2$ is used in a hydraulic press to exert a force of $10^7 \, dynes$ on the water. The cross-sectional area of the other piston which supports an object having a mass $2000 \, kg$ is:

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 hydraulic lift,the surface area of the input piston is $6 \ cm^2$ and that of the output piston is $1500 \ cm^2$. If $100 \ N$ force is applied to the input piston to raise the output piston by $20 \ cm$,then the work done is . . . . . . $kJ$.

$A$ hydraulic automobile lift is designed to lift vehicles of mass $5000\,kg$. The area of cross-section of the cylinder carrying the load is $250\,cm^2$. The maximum pressure the smaller piston would have to bear is [Assume $g = 10\,m/s^2$].

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A:$ When you squeeze one end of a tube to get toothpaste out from the other end,Pascal's principle is observed.
Reason $R:$ $A$ change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
In the light of the above statements,choose the most appropriate answer from the options given below: