A hydraulic automobile lift has input and output pistons with diameters of $10 \mathrm{cm}$ and $30 \mathrm{cm}.$ The lift is used to hold up a car with a weight of $144\times {10}^4 \mathrm{N}.$
(a) What is the force on the input piston?
(b) What pressure is applied on the input piston?

What will be the length of mercury column in a barometer tube when the atmospheric pressure is $75 \mathrm{cm}$ of mercury and the tube is inclined at an angle of $60°$ with the horizontal direction?

A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in the same level with $10 \mathrm{cm}$ of water in one $\mathrm{arm}$ and $12.5 \mathrm{cm}$ of spirit in the other. What is the specific gravity of spirit?

A U-tube in which the cross-sectional area of the limb on the left is one-third of the limb on the right contains mercury (density $13.6 \mathrm{g}/{\mathrm{cm}}^3$). The level of mercury in the narrow limb extends to distance of $30 \mathrm{cm}$ from the upper end of the tube. What will be the rise in the level of mercury in the right limb, if the left limb is filled to the top with water (neglect surface tension effects)?

Figure (b) shows the variation of pressure $\left(p\right)$ with depth $\left(h\right)$ along a vertical wall supporting two liquids of different densities as shown in Fig. (a). Identify the correct variation of pressure in the liquid of density ${\rho }_2.$

Water stands at a depth of $15 \mathrm{m}$ behind a reservoir dam. A horizontal pipe $4 \mathrm{cm}$ in diameter passes through the dam $6 \mathrm{m}$ below the surface $01$ water as shown. There is a plug which secures the pipe opening. Then find the friction between the plug and pipe wall.

A glass full of water has a bottom of area $20 {\mathrm{cm}}^2$, top of area $20 {\mathrm{cm}}^2$, height $20 \mathrm{cm}$ and volume half a litre.
(a) Find the force exerted by the water on the bottom.
(b) Considering the equilibrium of the water, find the resultant force exerted by the sides of the glass on the water. Atmospheric pressure $=1.00\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$, Density of water $=1000 \mathrm{kg} {\mathrm{m}}^{-3}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$. Take all numbers to be exact.

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