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CAIE A-Level Physics AS 4.3 Density and Pressure Questions

Practise calculating density, pressure and hydrostatic changes, explaining upthrust and applying Archimedes’ principle to floating or suspended bodies.

Syllabus
2028–2030
Course
Physics 9702
Level
AS

Exam points

  • use ρ = m/V to calculate or compare density, mass and volume for solids, liquids or composite materials
  • calculate pressure from force and area and use Δp = ρgΔh for a fluid column or pressure difference
  • explain hydrostatic pressure and derive or apply its dependence on density, gravitational field strength and depth
  • explain the origin of upthrust from the pressure difference across an immersed object
  • calculate upthrust with F = ρgV and apply Archimedes’ principle with force balance to floating or suspended bodies

Covered syllabus points

4.3.1—Density4.3.2—Pressure4.3.3—Derive, from the definitions of pressure and density, the equation4.3.4—The equation ∆p = ρg∆h4.3.5—The upthrust acting on an object in a fluid is due to a difference in4.3.6—The upthrust acting on an object in a fluid using the equation F = ρgV

Question 1

[Maximum number: 1]

The diagram shows the arrangement of atoms in a particular crystal.

Figure for Question 1 — CAIE A-Level Physics AS

Each atom is at the corner of a cube.
The mass of each atom is 3.5×10−25 kg3.5 \times 10^{-25} \mathrm{~kg}. The density of the crystal is 9.2×103 kg m−39.2 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}.
What is the shortest distance between the centres of two adjacent atoms?

A

3.8×10−29 m3.8 \times 10^{-29} \mathrm{~m}

B

6.2×10−15 m6.2 \times 10^{-15} \mathrm{~m}

C

3.4×10−10 m3.4 \times 10^{-10} \mathrm{~m}

D

3.0×10−9 m3.0 \times 10^{-9} \mathrm{~m}

Question 2

[Maximum number: 1]

Which expression for pressure is correct?

A

force per unit area

B

mass per unit area

C

mass per unit volume

D

weight per unit volume

Question 3

[Maximum number: 1]

The derivation of the pressure equation Δp=ρgΔh\Delta p=\rho g \Delta h uses a number of relationships between quantities.

Which relationship is not used in the derivation of this equation?

A

density = mass  volume =\frac{\text { mass }}{\text { volume }}

B

potential energy = mass × acceleration of free fall × height

C

pressure = force  area =\frac{\text { force }}{\text { area }}

D

weight = mass × acceleration of free fall

Question 4

[Maximum number: 1]

Four measuring cylinders are filled with the same liquid to the heights shown.

At which position is the pressure the greatest?

Figure for Question 4 — CAIE A-Level Physics AS
Figure for Question 4 — CAIE A-Level Physics AS
Figure for Question 4 — CAIE A-Level Physics AS
A
Option A shown in diagram

Option A shown in diagram

B
Option B shown in diagram

Option B shown in diagram

C
Option C shown in diagram

Option C shown in diagram

D
Option D shown in diagram

Option D shown in diagram

Question 5

[Maximum number: 1]

A ball falls through a liquid at a constant speed. It is acted upon by three forces: an upthrust, a drag force and its weight.

The liquid has a uniform density.
Which statement is correct?

A

The drag force increases with increasing depth.

B

The drag force is equal to the sum of the upthrust and weight.

C

The upthrust is constant with increasing depth.

D

The weight is greater than the sum of the drag force and the upthrust.

Question 6

[Maximum number: 1]

Two solid cylindrical objects X and Y are held fully submerged in a liquid, as shown.

Figure for Question 6 — CAIE A-Level Physics AS

The objects have the same volume. The density of the material of Y is twice the density of the material of X. Both objects are stationary.

Which statement is correct?

A

The force due to the liquid acting on the top surface of X is greater than that acting on the top surface of Y.

B

The pressure difference due to the liquid between the top and bottom surfaces of X is the same as that for Y .

C

The upthrust acting on X is the same as the upthrust acting on Y .

D

The weight of X is the same as the weight of Y.

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