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 $\text{ N}$)

$A$ 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

$A$ 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.

Write a short note on hydraulic brakes.

The diagram below shows a hydraulic lift. $A$ force is applied at side $1$ and an output force is generated at side $2$. Which of the following is true?

$A$ 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 . . . . . . $N$.