Water flows through two identical tubes $\mathrm{A}$ and $\mathrm{B}$. A volume $V_0$ of water passes through the tube $\mathrm{A}$ and $2V_0$ through $\mathrm{B}$ in a given time. Which of the following may be correct?

The heights of mercury surfaces in the two arms of the manometer shown in the figure are $2 \mathrm{cm}$ and $8 \mathrm{cm}$. Atmospheric pressure $=1.01\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$. Find
(a) The pressure of the gas in the cylinder and
(b) The pressure of mercury at the bottom of the U tube.
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The area of cross-section of the wider tube shown in the figure is $900 {\mathrm{cm}}^2$. If the boy standing on the piston weighs $45 \mathrm{kg}$, find the difference in the levels of the water in the two tubes.

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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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.
Suppose the glass is covered by a jar and the air inside the jar is completely pumped out.
(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 $=1·0\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$. Density of water $=1000 \mathrm{kg} {\mathrm{m}}^{-3}$ and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$. Take all numbers to be exact.
(c) Show that the answers do not change if a glass of different shape is used provided the height, the bottom area and the volume are unchanged.

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