Senior 2 practice book · Unit 4 of 10

Pressure in Solids and Liquids

50 questions that complete the Senior 2 quiz for this unit: 23 core and 27 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

A bigger, wider tank of water gives a bigger water pressure at the tap below it.Liquid pressure depends only on the depth below the surface, the density and g (P = hρg). A wider tank holds more water but, at the same depth, gives the same pressure.
Spreading the weight over a larger area reduces the force on the ground.The force (the weight) stays the same; it is the PRESSURE, force per unit area, that becomes smaller when the area is larger.
When we drink through a straw, our mouth pulls the liquid up.Sucking only lowers the air pressure inside the straw. The greater atmospheric pressure on the surface of the drink pushes the liquid up the straw.
A hydraulic jack makes the pressure bigger under the large piston, so it gives a bigger force.The pressure is the SAME everywhere in the liquid (Pascal's principle). The force is bigger on the large piston only because F = PA and its area is larger.
Pressure in a liquid acts only downwards, on the bottom of the container.At any point in a liquid, pressure acts equally in all directions: on the sides of the container, on the base and upwards on anything immersed.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Pressure in solids: P = F/A and the pascal
Increasing and reducing pressure in daily life (sharp tools, wide tracks, foundations)
Pressure units and conversions (cm² and mm² to m², kPa, MPa, N/cm², mmHg)
Liquid pressure P = hρg: depth, density, all directions, not the shape of the container
Total (absolute) pressure below a liquid surface: P = P_atm + hρg; gauge pressure
Applications of liquid pressure: dams, water towers, water supply, drips
Force due to liquid pressure on a surface (F = PA) and the upward push on a submerged body
Communicating vessels: a liquid finds its own level
U-tube with liquids that do not mix: h₁ρ₁ = h₂ρ₂
Manometers: measuring gas pressure and pressure differences
Atmospheric pressure: evidence for it and its change with altitude
Barometers: mercury and aneroid barometers, altimeters
Devices that work by atmospheric pressure: drinking straw, siphon, lift pump, suction cup
Pascal's principle and hydraulic machines (press, jack, brakes)

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 27 harder ones are marked ★ Challenge.

1True or false
Tilting the tube of a mercury barometer changes the vertical height of the mercury column above the dish.
Show answer
Answer: False
The vertical height is fixed by the atmospheric pressure; tilting only makes the mercury fill more of the tube's length.
Common mistakeLearners confuse the length of mercury along the tilted tube with its vertical height, which is what P = hρg uses.
2True or false · ★ Challenge
A camel's wide feet exert a smaller force on the sand than the narrow hooves of a donkey of the same weight.
Show answer
Answer: False
Both animals push down with a force equal to their (equal) weights. The camel's feet exert a smaller PRESSURE because the area is larger.
Common mistakeSaying 'true' mixes up force and pressure; a wider foot changes the pressure, not the force.
3True or false · ★ Challenge
If a teapot's spout opening is lower than the top of the pot, the pot can only be filled up to the level of the spout opening.
Show answer
Answer: True
The liquid in the pot and spout finds the same level; once it reaches the spout opening, extra water flows out.
Common mistakeAnswering false assumes the pot can be filled to the brim regardless; the connected spout limits the level.
4True or false
At the same depth, the pressure of water on the side wall of a tank is as large as the pressure on a horizontal surface.
Show answer
Answer: True
Pressure at a point in a liquid acts equally in all directions, so at the same depth it is the same on a side wall as on a floor.
Common mistakeMany learners think liquid pressure only pushes down; it pushes sideways and upwards just as strongly at that depth.
5True or false · ★ Challenge
A suction (lift) pump at the top of a well can raise water from at most about 10 m below it at sea level, and from less depth in Kigali.
Show answer
Answer: True
The atmosphere can only push water up until hρg equals P_atm: 100 000 ÷ (1000 × 10) = 10 m at sea level, and about 8.7 m where P_atm ≈ 87 kPa.
Common mistakeThinking a stronger pump could lift water from any depth is wrong; a suction pump only lowers the pressure, and the atmosphere does the pushing.
6True or false
The difference in liquid levels in a manometer depends on how wide its tubes are.
Show answer
Answer: False
The difference in levels is h = ΔP ÷ (ρg); it depends on the pressure difference and the liquid's density, not on the width of the tubes.
Common mistakeThinking a wider tube gives a smaller difference is the shape-of-container error; liquid pressure depends on height, not width.
7True or false · ★ Challenge
A dam holding back a lake 5 km long needs a thicker wall than an identical dam holding back a lake only 100 m long, if the water is equally deep in both.
Show answer
Answer: False
The pressure on a dam depends only on the depth of water (P = hρg), not on how far the lake stretches behind it.
Common mistakeThinking a bigger lake pushes harder is the 'amount of water' misconception; equal depth gives equal pressure on the wall.
8Fill in the blank
As you climb higher above sea level, atmospheric pressure ______.
Show answer
Answer: decreases
There is less air above you, so the weight of air on each square metre is smaller.
Common mistakeWriting 'increases' wrongly assumes being closer to the sky means more air above; the air column above becomes shorter.
9Multiple choice · ★ Challenge
Atmospheric pressure on the summit of Mount Karisimbi (about 4500 m) is much lower than in Kigali. The main reason is:
1. AGravity is much weaker on a mountain top, so the air there weighs nothing
2. BThere is less air above the summit, so less weight of air on each square metre
3. CThe cold air at the summit is lighter and presses less on the ground
4. DThe mountain blocks the air coming from above, so the pressure cannot reach it
Show answer
Answer: B. There is less air above the summit, so less weight of air on each square metre
Atmospheric pressure is caused by the weight of the air above a place; higher up there is a shorter, thinner column of air above.
Common mistakeChoosing 'gravity is much weaker' exaggerates a tiny effect; g at 4500 m is still almost 10 N/kg, but the column of air above is much shorter.
10True or false
In an ideal hydraulic press, the pressure under the large piston is greater than the pressure under the small piston.
Show answer
Answer: False
By Pascal's principle the pressure is the same throughout the liquid; the large piston gets a larger FORCE because F = PA.
Common mistakeAnswering true confuses force and pressure: the force is multiplied, the pressure is not.
11Short answer · ★ Challenge
A farmer empties a drum of water by using a siphon tube. Explain how the siphon works and state two conditions needed for it to work.
Show answer
Model answer: Once the tube is full of water, the water in the long outer arm is a taller column than in the short arm inside the drum, so the pressure at the outlet end is greater than atmospheric and water flows out; atmospheric pressure on the drum's surface keeps pushing water up into the tube. Conditions: the tube must first be completely full of water (no air), and the outlet must be lower than the water surface in the drum (and the bend not more than about 10 m above the surface).
Common mistakeA common error is to think the water flows 'uphill by itself'; it is atmospheric pressure on the drum's surface that pushes it over the bend.
12Multiple choice
When you drink juice through a straw, the juice rises because:
1. AYour mouth pulls the juice up the straw with a strong sucking force acting on the juice
2. BThe juice is less dense than the air inside the straw
3. CYour breath increases the air pressure on the juice in the cup
4. DYou lower the air pressure in the straw and atmospheric pressure pushes the juice up
Show answer
Answer: D. You lower the air pressure in the straw and atmospheric pressure pushes the juice up
Sucking removes air from the straw, so the pressure inside is lower; the larger atmospheric pressure on the juice's surface pushes it up.
Common mistakeChoosing 'your mouth pulls' is the main misconception; air can only push, and it is the outside atmosphere that does the pushing.
13Fill in the blank · ★ Challenge
A hydraulic lift at a garage in Nyabugogo has a small piston of radius 2 cm and a large piston of radius 12 cm. An effort of 150 N on the small piston supports a load of ______ N.
Show answer
Answer: 5400
Area ratio = (12 ÷ 2)² = 36. Load = 150 × 36 = 5400 N.
Common mistakeUsing the radius ratio 6 without squaring gives 900 N; area = πr², so the ratio of areas is the ratio of radii SQUARED.
14Fill in the blank
In a U-tube holding two liquids that do not mix, the ______ liquid stands in the taller column above the boundary level.
Show answer
Answer: less dense
h₁ρ₁ = h₂ρ₂, so a smaller density needs a greater height to give the same pressure.
Common mistakeWriting 'denser' reverses the idea: a dense liquid gives a large pressure with a SHORT column.
15Short answer · ★ Challenge
Explain how an aneroid barometer can be used as an altimeter by a pilot or a hiker climbing Mount Bisoke, and why it should be reset before each trip.
Show answer
Model answer: Atmospheric pressure falls as height increases, so the dial can be marked in metres of height instead of pascals: a lower pressure reading means a greater height. Because the weather also changes the air pressure from day to day, the altimeter must be set to the correct height at a known starting point before each trip, or it will give wrong heights.
Common mistakeForgetting that weather changes the pressure leads to believing an altimeter is always right; a change in weather can look like a change in height.
16Multiple choice · ★ Challenge
In Nyagatare the atmospheric pressure is 90 kPa. What is the greatest depth from which a hand suction pump at the top of a well can raise water? (water 1000 kg/m³, g = 10 N/kg)
1. A9 m
2. B90 m
3. C0.9 m
4. D10 m
Show answer
Answer: A. 9 m
h = P ÷ (ρg) = 90 000 ÷ (1000 × 10) = 9 m.
Common mistakeChoosing 10 m uses the sea-level value of about 100 kPa; Nyagatare is high above sea level, so its air pressure is lower.
17Multiple choice
A builder fills a long clear hose with water to mark the same height on two walls of a house. This works because:
1. AThe water surfaces at the two ends settle at the same horizontal level
2. BWater runs towards the lower end of the hose until that end is full
3. CThe water level is always higher at the wider end of the hose
4. DThe water surface is always higher at the end of the hose that holds more water
Show answer
Answer: A. The water surfaces at the two ends settle at the same horizontal level
In connected vessels a liquid at rest has the same pressure at the same level, so its free surfaces are at the same height.
Common mistakeChoosing 'higher where there is more water' is the amount-of-liquid error; the surfaces level out whatever the amount in each part.
18Multiple choice · ★ Challenge
A pressure sensor in a tank of cooking oil reads a liquid pressure of 6000 Pa at a depth of 0.75 m (g = 10 N/kg). What is the density of the oil?
1. A8000 kg/m³
2. B450 kg/m³
3. C80 kg/m³
4. D800 kg/m³
Show answer
Answer: D. 800 kg/m³
ρ = P ÷ (hg) = 6000 ÷ (0.75 × 10) = 6000 ÷ 7.5 = 800 kg/m³.
Common mistakeChoosing 8000 kg/m³ comes from dividing by h only and forgetting g; ρ = P/(hg).
19Fill in the blank
A pressure of 2.5 N/cm² is equal to ______ Pa.
Show answer
Answer: 25 000
1 m² = 10 000 cm², so 2.5 N/cm² = 2.5 × 10 000 = 25 000 N/m² = 25 000 Pa.
Common mistakeMultiplying by 100 instead of 10 000 (forgetting to square the 100 cm in a metre) gives 250 Pa.
20Multiple choice · ★ Challenge
On Lake Muhazi the atmospheric pressure is 88 kPa (water 1000 kg/m³, g = 10 N/kg). At what depth is the total pressure twice the atmospheric pressure?
1. A17.6 m
2. B88 m
3. C8.8 m
4. D0.88 m
Show answer
Answer: C. 8.8 m
Total = 2 × 88 kPa means the water adds 88 000 Pa: h = P ÷ (ρg) = 88 000 ÷ 10 000 = 8.8 m.
Common mistakeChoosing 17.6 m makes the WATER pressure equal to 176 kPa, forgetting that the air already gives the first 88 kPa.
21Multiple choice
Some water is boiled in an open metal tin, then the tin is sealed and cooled with cold water. It crushes. Why?
1. AThe cold water outside pulls the thin metal walls of the tin inwards as it cools them
2. BThe metal of the tin shrinks a lot when it is suddenly cooled
3. CThe air inside becomes heavier when cold and pulls the walls in
4. DThe steam condenses, so the pressure inside falls far below atmospheric pressure
Show answer
Answer: D. The steam condenses, so the pressure inside falls far below atmospheric pressure
Steam had pushed most of the air out; when it condenses the pressure inside becomes very low, and the atmosphere outside crushes the tin.
Common mistakeChoosing a 'pulling' answer is wrong because gases and liquids only push; the crush is caused by the outside air pushing harder than the inside.
22Multiple choice · ★ Challenge
A nurse at a health centre measures a blood pressure of 120 mmHg (mercury density 13 600 kg/m³, g = 10 N/kg). What is this in pascals?
1. AAbout 163 kPa
2. BAbout 16 kPa
3. CAbout 1.6 kPa
4. DAbout 1632 kPa
Show answer
Answer: B. About 16 kPa
120 mm = 0.12 m. P = hρg = 0.12 × 13 600 × 10 = 16 320 Pa ≈ 16 kPa.
Common mistakeChoosing 1.6 kPa comes from writing 120 mm as 0.012 m; 1 mm = 0.001 m, so 120 mm = 0.12 m.
23Multiple choice
A drip bag at a hospital is hung high above the patient's arm. Why?
1. AA higher bag holds more fluid, so the larger amount of fluid pushes harder into the vein
2. BThe air pressure is lower near the ceiling, so it pulls the fluid down
3. CThe fluid becomes denser when it is lifted higher above the arm
4. DThe greater height gives a greater liquid pressure to push fluid into the vein
Show answer
Answer: D. The greater height gives a greater liquid pressure to push fluid into the vein
Pressure at the needle = hρg, where h is the height of the fluid surface above the arm; a higher bag gives a larger h and pressure.
Common mistakeChoosing 'holds more fluid' confuses the amount of liquid with depth; only the height of the liquid surface above the needle matters.
24Short answer · ★ Challenge
Water for Kigali is pumped up to reservoirs on high hills before it flows to homes through pipes. Explain why the reservoirs are placed high, and why houses built almost as high as a reservoir often get a weak flow at their taps.
Show answer
Model answer: The pressure at a tap is P = hρg, where h is the height of the reservoir's water surface above the tap; a high reservoir gives a large h, so water is pushed out strongly in the low parts of the city. A house built almost as high as the reservoir has a very small h, so the pressure at its taps is small and the water flows weakly.
Common mistakeSaying the water is weak because it 'runs out' is wrong; the house is high up, so the depth of water above its taps, and hence the pressure, is small.
25Fill in the blank
Water at the bottom of a tank exerts a pressure of 8000 Pa on a base of area 0.5 m². The force on the base is ______ N.
Show answer
Answer: 4000
F = PA = 8000 × 0.5 = 4000 N.
Common mistakeDividing 8000 ÷ 0.5 = 16 000 N treats the formula as F = P/A; force is pressure TIMES area.
26Multiple choice · ★ Challenge
In a U-tube, 6 cm of mercury (13 600 kg/m³) above the common level balances a 68 cm column of liquid X in the other arm. What is the density of X?
1. A120 kg/m³
2. B12 000 kg/m³
3. C1200 kg/m³
4. D1360 kg/m³
Show answer
Answer: C. 1200 kg/m³
h₁ρ₁ = h₂ρ₂: 68 × ρ = 6 × 13 600 = 81 600, so ρ = 81 600 ÷ 68 = 1200 kg/m³.
Common mistakeChoosing 12 000 kg/m³ comes from a slip of a factor of 10; check that the less dense liquid has the TALLER column (68 cm against 6 cm).
27Multiple choice · ★ Challenge
A rectangular water tank has a base of 2 m × 1.5 m and holds water 1.2 m deep (water 1000 kg/m³, g = 10 N/kg, ignore air pressure). What force does the water exert on the base?
1. A12 000 N
2. B3600 N
3. C36 000 N
4. D18 000 N
Show answer
Answer: C. 36 000 N
P = hρg = 1.2 × 1000 × 10 = 12 000 Pa. A = 2 × 1.5 = 3 m². F = PA = 12 000 × 3 = 36 000 N.
Common mistakeChoosing 12 000 N stops at the pressure; force needs F = P × A, and the base area is 3 m².
28Multiple choice
Why are the foundations of a tall building in Kigali made much wider than its walls?
1. ATo spread the weight over a large area so the soil is not overloaded
2. BTo make the building heavier, so that it stays standing firmly in strong winds
3. CTo increase the pressure so the walls grip the soil more firmly
4. DTo reduce the weight that the building puts on the ground
Show answer
Answer: A. To spread the weight over a large area so the soil is not overloaded
A wide foundation gives a large area, so the pressure P = F/A on the soil is small enough for the soil to support.
Common mistakeChoosing 'reduce the weight' confuses force and pressure: the weight is unchanged, only the pressure falls.
29Multiple choice · ★ Challenge
A window of area 0.05 m² on a research submarine is 60 m below the sea surface (sea water 1030 kg/m³, g = 10 N/kg, ignore air pressure). What force does the water exert on the window?
1. A618 000 N
2. B30 900 N
3. C3090 N
4. D12 360 000 N
Show answer
Answer: B. 30 900 N
P = hρg = 60 × 1030 × 10 = 618 000 Pa. F = PA = 618 000 × 0.05 = 30 900 N.
Common mistakeChoosing 12 360 000 N divides the pressure by the area instead of multiplying; F = PA.
30Multiple choice
In a car's hydraulic brakes the piston in the master cylinder (at the pedal) is small and the pistons at the wheels are larger. Why?
1. AThe larger wheel pistons make the brake fluid flow faster to the wheels
2. BThe small pedal piston makes the pressure at the wheels much larger than at the pedal itself
3. CThe larger wheel pistons reduce the energy needed to stop the car
4. DThe same pressure on the larger wheel pistons gives larger forces on the brake pads
Show answer
Answer: D. The same pressure on the larger wheel pistons gives larger forces on the brake pads
The pressure is the same throughout the fluid; F = PA, so a larger piston area at each wheel gives a larger braking force.
Common mistakeChoosing 'pressure larger at the wheels' is the misconception that pressure is multiplied; only the force is.
31Multiple choice · ★ Challenge
A mercury barometer reads 60 cm at a hilltop school and 66 cm in the valley below (mercury 13 600 kg/m³, g = 10 N/kg). What is the difference in atmospheric pressure between the two places?
1. AAbout 82 kPa
2. BAbout 8.2 kPa
3. CAbout 0.82 kPa
4. DAbout 90 kPa
Show answer
Answer: B. About 8.2 kPa
Δh = 66 − 60 = 6 cm = 0.06 m. ΔP = Δhρg = 0.06 × 13 600 × 10 = 8160 Pa ≈ 8.2 kPa.
Common mistakeChoosing about 90 kPa calculates the valley's whole pressure (0.66 × 13 600 × 10) instead of the difference.
32Multiple choice
A water manometer is joined to a gas pipe. The water is 6 cm LOWER in the open arm than in the arm joined to the gas (g = 10 N/kg). The gas pressure is:
1. A600 Pa below atmospheric pressure
2. B600 Pa above atmospheric pressure
3. C6000 Pa above atmospheric pressure
4. DEqual to atmospheric pressure
Show answer
Answer: A. 600 Pa below atmospheric pressure
The atmosphere pushes the water down further in the open arm, so the gas pressure is smaller by hρg = 0.06 × 1000 × 10 = 600 Pa.
Common mistakeChoosing 'above' ignores which arm is lower; the side with the LOWER liquid surface has the greater pressure.
33Short answer · ★ Challenge
Describe how a thistle funnel covered with a thin rubber sheet and joined to a U-tube manometer can be used to show that, at a given depth, the pressure in water is the same in all directions. State what you would observe.
Show answer
Model answer: Lower the covered funnel into water to a fixed depth and note the difference in the manometer levels. Keeping the centre of the rubber sheet at the same depth, turn the funnel so the sheet faces up, down and sideways. The difference in levels stays the same, showing the pressure is the same in all directions; lowering the funnel deeper makes the difference larger.
Common mistakeA common error is to let the depth change while turning the funnel; the depth of the sheet must stay fixed or the test is not fair.
34Fill in the blank
A cow of weight 2000 N stands on soft ground and exerts a pressure of 50 000 Pa. The total area of its hooves touching the ground is ______ m².
Show answer
Answer: 0.04
A = F ÷ P = 2000 ÷ 50 000 = 0.04 m².
Common mistakeMultiplying F × P instead of dividing gives a huge 'area'; rearrange P = F/A to A = F/P.
35Short answer · ★ Challenge
A mechanic finds that a hydraulic car jack lifts poorly: pushing the handle moves the small piston a long way, but the car hardly rises. He finds air bubbles in the oil. Explain why the bubbles stop the jack from working well and what he should do.
Show answer
Model answer: Air is easily compressed, unlike oil. When the small piston pushes, much of its movement just squashes the air bubbles instead of passing the pressure on to the large piston, so the load hardly rises. He should remove the air (bleed the system) and refill it with oil.
Common mistakeSaying air is 'too light' misses the point; the problem is that gases are compressible, so pressure is not transmitted fully.
36Multiple choice
A square floor tile in a classroom measures 20 cm by 20 cm. What is its area in square metres?
1. A0.4 m²
2. B0.0004 m²
3. C400 m²
4. D0.04 m²
Show answer
Answer: D. 0.04 m²
Change the lengths first: 20 cm = 0.2 m, so A = 0.2 × 0.2 = 0.04 m² (or 400 cm² × 0.0001 = 0.04 m²).
Common mistakeChoosing 0.4 m² comes from dividing 400 cm² by 1000 instead of 10 000; 1 m² = 100 cm × 100 cm = 10 000 cm².
37Multiple choice · ★ Challenge
In an ideal hydraulic press an effort of 50 N pushes the small piston down 20 cm, and the load on the large piston rises 0.5 cm. Using work in = work out, what load is raised?
1. A1250 N
2. B200 N
3. C2000 N
4. D20 000 N
Show answer
Answer: C. 2000 N
Work in = 50 × 0.20 = 10 J. Work out = L × 0.005 = 10 J, so L = 10 ÷ 0.005 = 2000 N.
Common mistakeChoosing 20 000 N comes from writing 0.5 cm as 0.0005 m; 0.5 cm = 0.005 m.
38Fill in the blank
A pressure gauge on a water pipe shows how much the pressure is above atmospheric pressure. This reading is called the ______ pressure.
Show answer
Answer: gauge
Gauge pressure = total (absolute) pressure − atmospheric pressure.
Common mistakeCalling it the 'total' pressure is wrong: the atmosphere's pressure must still be added to get the total.
39Short answer · ★ Challenge
Spot the error. A learner writes: 'A sack of beans of weight 400 N rests on a base of area 800 cm², so P = 400 ÷ 800 = 0.5 Pa.' Explain the mistake and give the correct pressure.
Show answer
Model answer: The area was left in cm², so the answer is in N/cm², not pascals. 800 cm² = 800 × 0.0001 = 0.08 m², so P = 400 ÷ 0.08 = 5000 Pa (which is also 0.5 N/cm²).
Common mistakeDividing newtons by cm² and calling the answer pascals is wrong because 1 Pa is 1 N on 1 m², and 1 m² is 10 000 cm².
40Short answer
A rubber suction hook stays stuck to a smooth fridge door but quickly falls off a rough wall. Explain both observations.
Show answer
Model answer: Pressing the cup pushes most of the air out from under it, so the pressure inside the cup is lower than atmospheric pressure. The greater atmospheric pressure outside holds it against the door. On a rough wall air leaks in through the gaps until the pressures are equal, so nothing holds the hook.
Common mistakeSaying the cup 'sucks' onto the door is the usual error; it is held by the outside air pushing on it.
41Multiple choice · ★ Challenge
A 60 kg learner (g = 10 N/kg) first stands on one foot of sole area 150 cm², then lies flat on a mat with a contact area of 0.5 m². How many times smaller is the pressure when she lies down?
1. AAbout 3 times smaller
2. BAbout 333 times smaller
3. CAbout 33 times smaller
4. DAbout 0.03 times smaller
Show answer
Answer: C. About 33 times smaller
Standing: P = 600 ÷ 0.015 = 40 000 Pa. Lying: P = 600 ÷ 0.5 = 1200 Pa. 40 000 ÷ 1200 ≈ 33.
Common mistakeChoosing 333 comes from changing 150 cm² into 0.0015 m² instead of 0.015 m² (1 cm² = 0.0001 m²).
42Short answer · ★ Challenge
A learner blows into one arm of a water manometer and keeps a 45 cm difference between the levels (g = 10 N/kg). Calculate how much her lung pressure is above atmospheric pressure, and explain why a mercury manometer would be less suitable for this test.
Show answer
Model answer: Excess pressure = hρg = 0.45 × 1000 × 10 = 4500 Pa. In mercury (13.6 times denser) the same pressure gives only 0.45 ÷ 13.6 ≈ 3.3 cm, which is too small to read accurately; water gives a large, easily read difference for small pressures.
Common mistakeLearners often think mercury is always better; mercury suits LARGE pressures, but for small ones its column is too short to measure precisely.
43Short answer
The spout of a kettle or teapot is made as high as the top of the pot. Use the idea of communicating vessels to explain why.
Show answer
Model answer: The pot and the spout are connected vessels, so the water surface in the spout is at the same level as in the pot. If the spout were lower than the top, water would run out of the spout as soon as the level reached it, so the pot could never be filled.
Common mistakeA common answer is 'so the tea pours better'; the real reason is that the water level in the spout equals the level in the pot.
44Short answer · ★ Challenge
A pressure washer at a car wash in Remera pushes water out at 3.0 MPa through a nozzle of area 2 mm². Convert the area to m² and find the force of the water on the nozzle opening.
Show answer
Model answer: 1 mm² = 10⁻⁶ m², so A = 2 × 10⁻⁶ m². P = 3.0 MPa = 3.0 × 10⁶ Pa. F = PA = 3.0 × 10⁶ × 2 × 10⁻⁶ = 6 N.
Common mistakeThe common error is 1 mm² = 10⁻³ m²; a millimetre is 10⁻³ m, so a square millimetre is (10⁻³)² = 10⁻⁶ m².
45Short answer
A drawing pin has a broad, flat head and a very sharp point. Explain, using pressure, why each end has this shape.
Show answer
Model answer: The same force acts at both ends. The sharp point has a tiny area, so the pressure on the board is very large and the pin goes in easily. The broad head has a large area, so the pressure on the thumb is small and does not hurt.
Common mistakeLearners often say the point has 'more force'; the force is the same at both ends, only the area and therefore the pressure differ.
46Short answer · ★ Challenge
A diver's watch is safe up to a total pressure of 500 kPa. At sea, atmospheric pressure is 100 kPa (sea water 1030 kg/m³, g = 10 N/kg). Find the greatest depth at which the watch can be used.
Show answer
Model answer: Pressure the water may add = 500 − 100 = 400 kPa = 400 000 Pa. h = P ÷ (ρg) = 400 000 ÷ (1030 × 10) ≈ 38.8 m, so about 39 m.
Common mistakeUsing the full 500 kPa for the water gives about 49 m, which forgets that 100 kPa of the limit is already used by the atmosphere.
47Multiple choice
A swimming pool in Kigali is 4 m deep, and atmospheric pressure there is 87 kPa (water 1000 kg/m³, g = 10 N/kg). What is the total pressure at the bottom of the pool?
1. A127 kPa
2. B40 kPa
3. C91 kPa
4. D40 087 Pa
Show answer
Answer: A. 127 kPa
Water pressure = hρg = 4 × 1000 × 10 = 40 000 Pa = 40 kPa. Total = 87 + 40 = 127 kPa.
Common mistakeChoosing 40 kPa gives only the pressure due to the water; the air above the pool also presses on it, so P = P_atm + hρg.
48Short answer · ★ Challenge
A cube of side 0.1 m is held under water with its top face 0.2 m below the surface (water 1000 kg/m³, g = 10 N/kg, ignore air pressure). Calculate the force of the water on the top face and on the bottom face, and the resultant force on the cube due to the water.
Show answer
Model answer: Top: P = 0.2 × 1000 × 10 = 2000 Pa; F = 2000 × 0.01 = 20 N downwards. Bottom (0.3 m deep): P = 3000 Pa; F = 3000 × 0.01 = 30 N upwards. Resultant = 30 − 20 = 10 N upwards (the upthrust).
Common mistakeUsing the same depth for both faces gives zero; the bottom face is 0.1 m deeper, so the pressure and force there are larger.
49Multiple choice
A graph is drawn of the pressure due to a liquid (not counting the air above it) against the depth below its surface. What shape is it?
1. AA curve that levels off at large depths
2. BA straight line through the origin
3. CA horizontal line, as pressure is the same at all depths
4. DA straight line sloping downwards
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Answer: B. A straight line through the origin
P = hρg, and ρ and g are constant, so P ∝ h: a straight line through the origin.
Common mistakeChoosing a curve that levels off assumes deep water stops adding pressure; every extra metre of water adds the same ρg.
50Short answer · ★ Challenge
A learner pours oil into one arm of a U-tube containing water. He records: oil surface 22 cm above the bottom, water surface 20 cm above the bottom, oil–water boundary 4 cm above the bottom. He writes ρ(oil) = 1000 × 20 ÷ 22 = 909 kg/m³. Find his mistake and work out the correct density.
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Model answer: He measured the heights from the bottom of the tube instead of from the level of the oil–water boundary. Oil column = 22 − 4 = 18 cm; water column = 20 − 4 = 16 cm. ρ(oil) = 1000 × 16 ÷ 18 ≈ 889 kg/m³.
Common mistakeHeights must be measured from the common level of the boundary, because only the liquid above that level is unbalanced.