Why use a pressure difference in challenge items?

The faces are at different pressures, and the difference times the area gives the upthrust, explaining it rather than just quoting rho g V.

Why does saving force cost distance?

Work is force times distance, and in an ideal machine input work equals output work, so a smaller force must move further.

S4 Physics pressure and fluids paper 3: ten multi-step items

2026-11-10

Tutor Prep Guide · S4 Physics Pressure and Fluids

Ten items in DSE style, linking pressure difference, upthrust, density and U-tubes in multi-step work.

Direct answers　Items 01 to 03 use pressure difference for upthrust and dams, 04 to 06 cover apparent weight and density, 07 to 09 U-tubes and bubbles. Allow 25 minutes.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S4 Physics Pressure and Fluids
Level	S4

02　Questions (10 items)

FoundationA cube of side 0.1 m is fully in water with its top face at 0.5 m depth. Find the pressure on the top and bottom faces and the upthrust.
FoundationA brick 20 cm by 10 cm by 5 cm weighs 20 N. Find the largest and smallest pressure it can exert.
FoundationA tank surface is 8 m above a tap. Find the water pressure at the tap.
IntermediateA jack has a small piston of 0.004 m squared under 200 N and a large piston of 0.02 m squared. Find the force it raises.
IntermediateAn object weighs 5 N in air and 3 N when fully in water. Find the upthrust, its volume and its density.
IntermediateA dam holds water 10 m deep over a 20 m wide face. Find the average pressure and the total force.
ChallengeA 0.2 m water column balances a 0.25 m oil column in a U-tube. Find the density of the oil.
ChallengeA diver at 30 m releases a bubble. By what factor does its volume grow at the surface? (100000 Pa per 10 m, 1 atm at the surface)
ChallengeAn iceberg of volume 0.02 m cubed floats in sea water. Find the exposed volume (ice 900, sea water 1030 kg per cubic metre).
Error redoA pupil says a hydraulic press saves both force and work. What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	5000 Pa; 6000 Pa; upthrust 10 N	The 1000 Pa difference times the 0.01 m squared face gives 10 N, matching rho g V.
2	Largest 4000 Pa; smallest 1000 Pa	The smallest face of 0.005 m squared gives 4000 Pa and the largest of 0.02 m squared gives 1000 Pa.
3	80000 Pa	P = rho x g x h = 1000 x 10 x 8 = 80000 Pa; only the height difference matters.
4	1000 N, about 100 kg	Pressure = 200 / 0.004 = 50000 Pa, and times 0.02 m squared gives 1000 N.
5	2 N; 0.0002 m cubed; 2500 kg per cubic metre	Upthrust is 2 N, so the volume is 2 / 10000 = 0.0002 m cubed, and 0.5 kg over that volume gives 2500.
6	50000 Pa; about 10000000 N	Use half the depth, 5 m, for 50000 Pa, then times the 200 m squared face for ten million newtons.
7	800 kg per cubic metre	The pressure at the base is the same on both sides: 1000 x 0.2 = rho x 0.25, so rho is 800.
8	About 4 times	At 30 m the total pressure is 400000 Pa, four times the surface value, so the volume becomes four times larger.
9	About 0.0025 m cubed	The submerged fraction is 900 / 1030, about 0.874, so roughly 12.6 percent is exposed.
10	A press multiplies force only: if the force grows 50 times, the piston moves 50 times less.	In an ideal press the input work equals the output work, so saving force always costs distance.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

Book a Physics tutor Tutor Registration →

Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.