Senior 3 practice book · Unit 5 of 10

Atmospheric Pressure and Archimedes' Principles

50 questions that complete the Senior 3 quiz for this unit: 20 core and 30 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

Sucking pulls a drink up a straw.There is no 'pulling' force from a low pressure. Sucking lowers the air pressure inside the straw, and the greater atmospheric pressure on the surface of the drink pushes it up.
Air weighs nothing, so it cannot press on anything.One cubic metre of air has a mass of about 1 kg. The column of air above each square metre of ground weighs about 100 000 N at sea level, and this weight causes atmospheric pressure.
Atmospheric pressure only pushes downwards.Pressure in a fluid acts equally in all directions, so air pushes up, down and sideways. That is why an upturned card can hold water in a glass.
The deeper an object sinks, the larger the upthrust on it.Once an object is completely under the surface, the volume of liquid it displaces no longer changes, so the upthrust stays the same at any depth.
Upthrust depends on how heavy the object is.Upthrust depends only on the volume of fluid displaced and the fluid's density. A piece of wood and a piece of iron of equal volume, both fully under water, feel the same upthrust.

What this unit covers

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

Atmospheric pressure: its cause, its size and how it changes with altitude
Measuring atmospheric pressure: mercury and water barometers, aneroid barometer, p = hρg
Uses of atmospheric pressure: straw, pipette, sucker, siphon, lift pump, vacuum cleaner
Demonstrating atmospheric pressure: collapsing can, Magdeburg hemispheres, upturned glass
Pressure in liquids: p = hρg, total pressure at a depth, dams and water towers
Measuring gas pressure with a manometer; gauge and absolute pressure
Atmospheric pressure, weather and the human body (breathing, ears, high altitude)
Archimedes' principle and calculating upthrust (U = ρVg)
Verifying Archimedes' principle with an overflow (eureka) can; volume by displacement
Apparent weight: finding density and relative density by weighing in air and in a liquid
Floating and sinking: law of flotation and the fraction submerged
Applications: ships and load lines, submarines, hydrometers, balloons

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 30 harder ones are marked ★ Challenge.

1True or false
Atmospheric pressure acts only downwards, because it is caused by the weight of the air.
Show answer
Answer: False
Pressure in a fluid acts equally in all directions at a point, so air also pushes upwards and sideways.
Common mistakeLinking 'weight' with 'downwards only' forgets that air molecules collide with surfaces facing any direction.
2True or false · ★ Challenge
When more passengers climb into a floating canoe, the upthrust on the canoe increases.
Show answer
Answer: True
The canoe sinks a little deeper and displaces more water until the upthrust equals the new, larger weight.
Common mistakeThinking the upthrust is fixed for a given canoe forgets that it depends on the volume under water.
3True or false · ★ Challenge
When an object floats partly submerged in a full eureka can, the volume of water that overflows equals the whole volume of the object.
Show answer
Answer: False
Only the submerged part displaces water, so the overflow equals the volume under the surface.
Common mistakeAssuming the overflow is always the object's whole volume forgets that a floating object is only partly under water.
4True or false
A stone that is completely under water feels a larger upthrust when it is lowered deeper.
Show answer
Answer: False
Once fully submerged it displaces the same volume of water at every depth, so the upthrust is unchanged.
Common mistakeLinking upthrust to depth confuses it with pressure; pressure rises with depth, but the difference between top and bottom stays the same.
5True or false · ★ Challenge
Oil pours smoothly from a closed tin when a second hole is made in the lid, because air can then enter and its pressure pushes on the oil.
Show answer
Answer: True
With one hole, the pressure inside falls as oil leaves, so it glugs; a second hole lets air in to keep atmospheric pressure inside.
Common mistakeThinking the second hole only 'lets oil out faster' misses the role of air entering the tin.
6True or false · ★ Challenge
The pressure at the bottom of a water tank depends on the depth of the water, not on how wide the tank is.
Show answer
Answer: True
p = hρg contains only depth, density and g; a wide tank has more weight but spread over a larger base.
Common mistakeThinking a bigger tank always gives a bigger pressure at the bottom confuses force with pressure.
7True or false
A glass full of water, covered with a card and turned upside down, keeps the water in because air pressure pushes up on the card.
Show answer
Answer: True
The upward atmospheric pressure on the card is far larger than the pressure of the water column pushing down on it.
Common mistakeThinking the card is 'stuck' by the water like glue misses the upward push of the air.
8True or false · ★ Challenge
A helium balloon stops rising at a certain height, partly because the air there is less dense, so the upthrust on it becomes smaller.
Show answer
Answer: True
Upthrust = ρ_air V g; as ρ_air falls with height, the upthrust falls until it equals the balloon's weight.
Common mistakeThinking a balloon rises forever ignores that upthrust depends on the density of the surrounding air.
9True or false
A ballpoint pen may leak in an aeroplane as it climbs, because the air pressure outside becomes lower than that of the air trapped inside the pen.
Show answer
Answer: True
The trapped air at higher pressure pushes the ink out when the outside pressure falls.
Common mistakeBlaming the cold or the vibration misses the pressure difference that drives the ink out.
10Multiple choice · ★ Challenge
How does a submarine come back up to the surface?
1. AIts engine pushes water down to make the upthrust bigger
2. BWater is pumped into its tanks so the upthrust grows
3. CAir forces water out of its tanks, so its weight falls
4. DIts metal hull becomes less dense as it rises up
Show answer
Answer: C. Air forces water out of its tanks, so its weight falls
With water blown out of the ballast tanks the submarine's weight is less than the (unchanged) upthrust, so it rises.
Common mistakeChoosing 'water pumped in' is the way to dive; filling the tanks makes the submarine heavier.
11Fill in the blank · ★ Challenge
A tyre gauge reads the pressure above atmospheric (the gauge pressure). The absolute pressure in the tyre = gauge pressure + ______ pressure.
Show answer
Answer: atmospheric
The gauge reads zero in open air, so the air's own pressure must be added to find the total.
Common mistakeForgetting to add atmospheric pressure gives a total that is about 1 × 10⁵ Pa too small.
12True or false
When the gas pressure on one side of a manometer equals the atmospheric pressure, the two liquid levels are at the same height.
Show answer
Answer: True
Equal pressures on both surfaces give no level difference (h = 0).
Common mistakeThinking the gas side must always be lower forgets that the levels only differ when the pressures differ.
13Multiple choice · ★ Challenge
A siphon is used to empty a fish tank into a bucket on the floor. Which change makes the water flow faster?
1. ARaising the bucket closer to the tank
2. BPlacing the bucket lower below the tank
3. CUsing a tube with a higher bend at the top
4. DUsing a narrower tube for the siphon
Show answer
Answer: B. Placing the bucket lower below the tank
The flow is driven by the height difference between the water surface in the tank and the outlet; lowering the bucket increases it.
Common mistakeChoosing a higher bend misunderstands the siphon: a higher top makes the flow harder, and too high stops it.
14Fill in the blank
A submarine dives when its ballast tanks are filled with ______, which makes it heavier than the upthrust.
Show answer
Answer: water
Letting sea water into the tanks increases its weight while its volume, and so the upthrust, stays the same.
Common mistakeAnswering 'air' reverses the process; air in the tanks makes the submarine rise.
15Multiple choice · ★ Challenge
Your ears 'pop' when a bus drives quickly down from Musanze to the lower land near Kigali. What is the cause?
1. AOutside air pressure falls and the eardrum bulges out
2. BThe air gets warmer, which makes the eardrum expand
3. CEngine vibration shakes the bones of the middle ear
4. DOutside air pressure rises and pushes the eardrum in
Show answer
Answer: D. Outside air pressure rises and pushes the eardrum in
Going down, the outside pressure increases while the air behind the eardrum is still at the lower pressure, until a tube opens to equalise them.
Common mistakeChoosing 'outside pressure falls' applies the rule for going up; going down means more air above, so higher pressure.
16Multiple choice · ★ Challenge
A small bubble of air gets into the space at the top of a mercury barometer. What happens to the reading?
1. AIt falls, as the trapped air presses down on the mercury
2. BIt rises, as the air adds its height to the mercury column
3. CIt stays the same, as the top space plays no part in it
4. DIt stays the same, as long as the tube is kept vertical
Show answer
Answer: A. It falls, as the trapped air presses down on the mercury
The space should be a vacuum; trapped air exerts a pressure on top of the column, so a shorter column balances the atmosphere.
Common mistakeChoosing 'stays the same' forgets that the barometer works only if there is no pressure above the mercury.
17Fill in the blank
Relative density has no unit, because it is the ratio of the density of a substance to the density of ______.
Show answer
Answer: water
Both densities have the unit kg/m³, so the units cancel.
Common mistakeAnswering 'air' uses the wrong reference; relative density is always compared with water.
18Multiple choice · ★ Challenge
In the Magdeburg hemispheres demonstration, two metal hemispheres are put together and the air is pumped out. Why are they then very hard to pull apart?
1. AThe vacuum inside pulls them together like a strong magnet
2. BAir outside pushes them together; nothing pushes back inside
3. CThe rubber seal between them sticks like glue once it is dry
4. DThe hemispheres become much heavier with no air inside
Show answer
Answer: B. Air outside pushes them together; nothing pushes back inside
With the air removed there is almost no pressure inside, so atmospheric pressure on the outside gives a large inward force.
Common mistakeChoosing 'the vacuum pulls' gives a vacuum a force it does not have; only the outside air pushes.
19Fill in the blank
When the air is pumped out of a sealed oil tin, the tin is crushed by the ______ pressure acting on its outside.
Show answer
Answer: atmospheric (air)
With little air inside, nothing balances the push of the air outside.
Common mistakeAnswering 'vacuum pressure' suggests the empty space does the crushing; it is the outside air.
20Multiple choice · ★ Challenge
Ice has a density of 920 kg/m³. What percentage of a floating block of ice is below the surface of fresh water?
1. A92%
2. B8%
3. C50%
4. D100%
Show answer
Answer: A. 92%
Floating: weight = upthrust, so ρ_ice V = ρ_water V_sub and V_sub ÷ V = 920 ÷ 1000 = 0.92 = 92%.
Common mistakeChoosing 8% gives the part ABOVE the water, not the part below.
21Multiple choice
What does a U-tube manometer measure?
1. AThe difference between a gas pressure and the air pressure
2. BThe total weight of the gas inside a closed cylinder
3. CThe temperature of a gas from how much the gas expands
4. DThe density of the liquid that is placed in the U-tube
Show answer
Answer: A. The difference between a gas pressure and the air pressure
The difference in liquid levels h gives the pressure difference hρg between the gas and the atmosphere.
Common mistakeChoosing 'the weight of the gas' confuses pressure with weight; a manometer compares two pressures.
22Multiple choice · ★ Challenge
A boat on Lake Kivu, with its crew, has a mass of 300 kg. What volume of water does it displace when floating? (Density of water 1000 kg/m³)
1. A3.0 m³
2. B0.30 m³
3. C3000 m³
4. D0.030 m³
Show answer
Answer: B. 0.30 m³
Floating: mass of water displaced = 300 kg, so V = m ÷ ρ = 300 ÷ 1000 = 0.30 m³.
Common mistakeChoosing 3000 m³ multiplies the mass by g (300 × 10) as if finding a weight; the volume is just the mass divided by the density, 300 ÷ 1000.
23Fill in the blank · ★ Challenge
Over two days a school barometer falls from 76.0 cm to 74.5 cm of mercury. Taking the density of mercury as 13 600 kg/m³ and g = 10 N/kg, the fall in pressure is ______ Pa.
Show answer
Answer: 2040
Δp = Δh ρ g = 0.015 × 13 600 × 10 = 2040 Pa.
Common mistakeUsing Δh = 1.5 instead of 0.015 m gives an answer 100 times too big; change cm to m first.
24Fill in the blank
The volume of an irregular stone is found by lowering it into water in a measuring cylinder: volume = final reading − ______ reading.
Show answer
Answer: initial (first)
The rise in the water level equals the volume of the stone.
Common mistakeUsing only the final reading gives the volume of water plus stone, not the stone.
25Short answer · ★ Challenge
Explain why a manometer for the high pressure in a gas cylinder uses mercury, while one for the low pressure of a laboratory gas supply uses water.
Show answer
Model answer: Mercury is 13.6 times denser than water, so a given pressure difference gives a level difference 13.6 times smaller; large pressures can then be measured with a tube of sensible length. For small pressures water gives a much larger level difference, which can be read more precisely.
Common mistakeSaying mercury is used because it is 'stronger' gives no physics; the key is the density in h = p ÷ (ρg).
26Short answer · ★ Challenge
Explain why the cabins of aeroplanes flying at 10 km above the ground are pressurised.
Show answer
Model answer: At 10 km the air pressure is very low, so each breath contains too little oxygen and passengers could lose consciousness. Gases in the body would also expand painfully. Pumping air in keeps the cabin at a comfortable pressure, like that of a town on a high plateau.
Common mistakeSaying the cabin is pressurised 'to keep the plane up' confuses breathing needs with flight.
27Multiple choice
What is the purpose of the load line (Plimsoll mark) painted on the side of a cargo ship?
1. AIt shows the greatest speed at which the ship may safely travel
2. BIt shows the depth of water under the ship's bottom
3. CIt shows where the engine pushes against the water
4. DIt shows how deep the ship may safely float when loaded
Show answer
Answer: D. It shows how deep the ship may safely float when loaded
If the loaded ship sits lower than the mark, it carries too much and may sink in rough water.
Common mistakeChoosing 'the depth of water under the ship' confuses the ship's own draught with the depth of the lake or sea.
28Short answer · ★ Challenge
A hiker closes an empty plastic water bottle tightly at the top of Mount Karisimbi and carries it down to Musanze. The bottle is found crushed. Explain why.
Show answer
Model answer: The bottle was sealed where the air pressure is low, so the air inside stays at that low pressure. Lower down there is more air above, so the outside pressure is higher. The greater pressure outside pushes the walls inwards and crushes the bottle.
Common mistakeSaying 'the cold crushed it' or 'the air inside was sucked out' misses the pressure difference between outside and inside.
29Multiple choice
In an experiment to verify Archimedes' principle with an overflow (eureka) can, what must be done before the object is lowered into the can?
1. AFill it to exactly half of its height with clean water
2. BEmpty it completely so that no water is wasted
3. CFill it until water just stops dripping from the spout
4. DFill it with water and then close the spout
Show answer
Answer: C. Fill it until water just stops dripping from the spout
Then every bit of water the object displaces flows out of the spout and can be collected.
Common mistakeChoosing 'half full' means the first displaced water only raises the level and is never collected.
30Multiple choice · ★ Challenge
The water surface in a school's tank on a tower is 18 m above a tap. What is the pressure of the water at the tap, above atmospheric pressure? (Density of water 1000 kg/m³, g = 10 N/kg)
1. A1.8 × 10⁴ Pa
2. B2.8 × 10⁵ Pa
3. C180 Pa
4. D1.8 × 10⁵ Pa
Show answer
Answer: D. 1.8 × 10⁵ Pa
p = hρg = 18 × 1000 × 10 = 1.8 × 10⁵ Pa.
Common mistakeChoosing 2.8 × 10⁵ Pa adds atmospheric pressure, but the question asks for the pressure above atmospheric.
31Multiple choice
A piece of wood and a piece of iron of exactly the same volume are both held completely under water. Which feels the larger upthrust?
1. ABoth feel the same upthrust
2. BThe iron, because it is heavier
3. CThe wood, because wood floats
4. DThe iron, because it is denser
Show answer
Answer: A. Both feel the same upthrust
Upthrust = weight of water displaced; equal volumes displace equal amounts of water.
Common mistakeChoosing 'the wood, because it floats' mixes up upthrust with floating; the wood floats because its weight is smaller, not because its upthrust is larger.
32Short answer · ★ Challenge
An egg sinks in tap water but floats in very salty water. Explain this in terms of density and upthrust, and say how you could make the egg stay still in the middle of the water.
Show answer
Model answer: The egg is denser than tap water, so even fully under water the upthrust is less than its weight. Salt water is denser, so the upthrust on the egg is larger and becomes greater than its weight, so it floats. By adding fresh water to the salty water little by little, you can make the liquid's density equal to the egg's; then upthrust equals weight when fully submerged and it stays where it is.
Common mistakeSaying the salt 'pushes the egg up' or makes the egg lighter misses that it is the liquid's density that changes.
33Short answer · ★ Challenge
A jerrycan full of water has three small holes, one near the top, one in the middle and one near the bottom. Describe and explain what you would see.
Show answer
Model answer: Water spurts out of all three holes, but the jet from the bottom hole goes furthest and the top one least far. The pressure in a liquid increases with depth (p = hρg), so the water at the bottom hole is pushed out hardest.
Common mistakeSaying all jets are the same ignores that the depth of water above each hole is different.
34Multiple choice
An empty sealed plastic bottle floats high in a pond. When half filled with sand it floats much lower. Why?
1. AThe sand makes the water around it less dense
2. BIts volume rose, so it must displace less water
3. CIts weight rose, so it must displace more water
4. DThe upthrust fell when the sand was put in
Show answer
Answer: C. Its weight rose, so it must displace more water
A floating body displaces its own weight of water; a heavier bottle must push aside more water, so it floats lower.
Common mistakeChoosing 'the upthrust fell' is the reverse: the upthrust increased to match the larger weight.
35Multiple choice · ★ Challenge
Atmospheric pressure on the shore of Lake Kivu is about 8.5 × 10⁴ Pa. What is the mass of the column of air above each square metre of the shore? (g = 10 N/kg)
1. A85 000 kg
2. B850 kg
3. C8500 kg
4. D8.5 kg
Show answer
Answer: C. 8500 kg
Weight of air on 1 m² = pA = 8.5 × 10⁴ × 1 = 85 000 N; mass = W ÷ g = 85 000 ÷ 10 = 8500 kg.
Common mistakeChoosing 85 000 kg forgets to divide the weight in newtons by g to get the mass.
36Multiple choice
A little water is boiled in an open metal can. The can is then sealed and cooled with cold water, and it collapses. Why?
1. AThe steam condenses, so the pressure inside drops very low
2. BThe cold water makes the metal contract until the can is crushed
3. CThe steam inside pulls the walls inwards as it cools and condenses
4. DThe air outside becomes much heavier as it cools down
Show answer
Answer: A. The steam condenses, so the pressure inside drops very low
Steam pushed the air out; when it condenses, little gas is left inside, so the atmospheric pressure outside crushes the can.
Common mistakeChoosing 'the steam pulls the walls' imagines a pulling force; the can is pushed in by the air outside.
37Multiple choice · ★ Challenge
In a eureka-can experiment a learner finds an upthrust of 1.2 N, but the overflow water weighs only 0.9 N. What is the most likely cause?
1. AThe stone was much denser than the water in the eureka can
2. BThe beaker was weighed before the experiment started
3. CThe spring balance was hung from a stand instead of a hand
4. DThe can was not full to the spout before the stone went in
Show answer
Answer: D. The can was not full to the spout before the stone went in
If the can was not full, some displaced water only raised the level in the can and never overflowed.
Common mistakeChoosing 'the stone was denser' gives no error: Archimedes' principle holds for objects of any density.
38Multiple choice · ★ Challenge
A fish farmer lowers a pressure sensor into Lake Muhazi, where the air pressure is about 8.6 × 10⁴ Pa. At what depth will the sensor read a total pressure double its reading at the surface? (Density of water 1000 kg/m³, g = 10 N/kg)
1. A17 m
2. B4.3 m
3. C8.6 m
4. D86 m
Show answer
Answer: C. 8.6 m
The water must add 8.6 × 10⁴ Pa: h = p ÷ (ρg) = 8.6 × 10⁴ ÷ (1000 × 10) = 8.6 m.
Common mistakeChoosing 17 m makes the water alone supply twice atmospheric pressure, forgetting that the air already supplies one atmosphere.
39Multiple choice
Why is the wall of a dam built much thicker at the bottom than at the top?
1. AWater at the bottom is colder and denser than at the top
2. BThe top of the wall has to carry the weight of the road
3. CWater pressure is greatest at the deepest point
4. DThick walls at the bottom stop the water from evaporating
Show answer
Answer: C. Water pressure is greatest at the deepest point
Liquid pressure p = hρg increases with depth, so the bottom of the wall must withstand the largest force.
Common mistakeChoosing 'colder, denser water' gives a small effect; the main cause is the depth h in p = hρg.
40Multiple choice · ★ Challenge
A necklace said to be pure gold weighs 0.386 N in air and 0.366 N when fully under water. Pure gold has a density of 19 300 kg/m³. What do the results show?
1. AIt is not pure: its density is 1050 kg/m³
2. BIt is not pure: its density is 18 300 kg/m³
3. CIt is not pure: its density is 52 kg/m³
4. DIt is pure: its density is 19 300 kg/m³
Show answer
Answer: D. It is pure: its density is 19 300 kg/m³
Upthrust = 0.386 − 0.366 = 0.020 N; relative density = 0.386 ÷ 0.020 = 19.3, so density = 19 300 kg/m³.
Common mistakeChoosing 18 300 kg/m³ divides the weight in water (0.366 N) by the upthrust; it must be the weight in air.
41Multiple choice · ★ Challenge
A water manometer is connected to a laboratory gas tap. The water on the open side stands 12 cm higher than on the gas side. Atmospheric pressure in the laboratory is 9.0 × 10⁴ Pa. What is the gas pressure? (Density of water 1000 kg/m³, g = 10 N/kg)
1. A1.2 × 10³ Pa
2. B9.12 × 10⁴ Pa
3. C8.88 × 10⁴ Pa
4. D2.1 × 10⁵ Pa
Show answer
Answer: B. 9.12 × 10⁴ Pa
Excess pressure = hρg = 0.12 × 1000 × 10 = 1200 Pa; gas pressure = 90 000 + 1200 = 9.12 × 10⁴ Pa.
Common mistakeChoosing 8.88 × 10⁴ Pa subtracts the excess; the gas pushed the water up the open side, so its pressure is higher than the air's.
42Short answer
Explain why a hydrometer has a weighted bulb, a wide body and a narrow stem.
Show answer
Model answer: The weight (lead shot) at the bottom keeps it floating upright. The wide body displaces most of the liquid needed to float. The narrow stem means a small change in the liquid's density gives a large change in how far it sinks, so the instrument is sensitive.
Common mistakeSaying the stem is narrow 'to save glass' misses its purpose of making the readings spread out.
43Multiple choice · ★ Challenge
A crane lifts a concrete block of volume 0.040 m³ (density 2400 kg/m³) from the bottom of a pond. By how much is the force needed less while the block is still completely under water? (Density of water 1000 kg/m³, g = 10 N/kg)
1. A960 N
2. B400 N
3. C560 N
4. D4.0 N
Show answer
Answer: B. 400 N
The force is less by the upthrust: U = ρ_water V g = 1000 × 0.040 × 10 = 400 N.
Common mistakeChoosing 560 N gives the apparent weight (960 − 400), which is the force needed, not the amount it is reduced by.
44Short answer
Explain how an aneroid barometer can be used as an altimeter in an aeroplane.
Show answer
Model answer: Atmospheric pressure falls in a known way as height increases. The aneroid's sealed box expands as the pressure falls and moves a pointer, so the scale can be marked in metres of height instead of pascals.
Common mistakeSaying it 'measures height directly' misses that it measures pressure, which is then converted to height.
45Short answer · ★ Challenge
A learner plans to use a siphon to move water from a reservoir over a hill 15 m high to a farm on the other side. Explain why this cannot work. (Atmospheric pressure there ≈ 9.0 × 10⁴ Pa, density of water 1000 kg/m³, g = 10 N/kg)
Show answer
Model answer: Atmospheric pressure can push water up only to h = p ÷ (ρg) = 9.0 × 10⁴ ÷ (1000 × 10) = 9.0 m. At the top of a 15 m bend the water column breaks and the siphon stops; the bend must be less than about 9 m above the water surface.
Common mistakeThinking a siphon works over any height forgets that air pressure, which pushes the water up the first side, has a limit.
46Multiple choice
Two mercury barometers stand side by side in the same laboratory; the tube of one is twice as wide as the other. How do their readings compare?
1. AThe wide tube's column is half as high
2. BThe wide tube's column is twice as high
3. CThe narrow tube's column is a quarter as high
4. DBoth columns have the same vertical height
Show answer
Answer: D. Both columns have the same vertical height
p = hρg does not depend on the area of the tube, so the same air pressure holds up the same height of mercury.
Common mistakeChoosing 'half as high' thinks a wider column is heavier and so shorter, but the larger weight acts on a larger area, giving the same pressure.
47Short answer · ★ Challenge
A pair of Magdeburg hemispheres has a circular rim of radius 0.10 m. All the air is pumped out. Estimate the force needed to pull them apart when the atmospheric pressure is 1.0 × 10⁵ Pa.
Show answer
Model answer: Area of the circle A = πr² = 3.14 × 0.10² ≈ 0.031 m². Force F = pA = 1.0 × 10⁵ × 0.031 ≈ 3.1 × 10³ N, about the weight of a 310 kg mass.
Common mistakeUsing the diameter 0.20 m in πr² gives a force four times too large; the formula needs the radius.
48Short answer · ★ Challenge
A stone weighs 2.6 N in air and 1.6 N when fully under water in a eureka can. The beaker that collects the overflow weighs 0.80 N empty and 1.80 N with the water. Show that these results support Archimedes' principle.
Show answer
Model answer: Upthrust = 2.6 − 1.6 = 1.0 N. Weight of water displaced = 1.80 − 0.80 = 1.0 N. The upthrust equals the weight of the water displaced, as Archimedes' principle states.
Common mistakeComparing the stone's weight in air with the weight of the overflow is wrong; it is the LOSS of weight that equals the overflow's weight.
49Multiple choice
A farmer wants the volume of an irregular stone but has no measuring cylinder. On a spring balance the stone reads 8.0 N in air and 5.0 N hanging fully under water in a bucket. What is its volume? (Density of water 1000 kg/m³, g = 10 N/kg)
1. A8.0 × 10⁻⁴ m³
2. B3.0 × 10⁻⁴ m³
3. C5.0 × 10⁻⁴ m³
4. D3.0 × 10⁻³ m³
Show answer
Answer: B. 3.0 × 10⁻⁴ m³
Upthrust = 8.0 − 5.0 = 3.0 N = ρVg, so V = 3.0 ÷ (1000 × 10) = 3.0 × 10⁻⁴ m³.
Common mistakeChoosing 8.0 × 10⁻⁴ m³ uses the weight in air; only the upthrust tells us the volume of water displaced.
50Short answer · ★ Challenge
A dairy checks milk for added water. A sinker weighs 3.00 N in air, 2.00 N in water and 1.97 N in a milk sample. Find the relative density of the milk and decide whether water has been added (pure milk has a relative density of about 1.03).
Show answer
Model answer: Upthrust in water = 3.00 − 2.00 = 1.00 N; upthrust in milk = 3.00 − 1.97 = 1.03 N. Relative density = 1.03 ÷ 1.00 = 1.03, the same as pure milk, so no water has been added.
Common mistakeDividing the readings in the liquids (1.97 ÷ 2.00) instead of the upthrusts gives a meaningless ratio.