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Density and pressure

4.3

What the syllabus asks of you

  • define and use density
  • define and use pressure
  • derive, from the definitions of pressure and density, the equation for hydrostatic pressure ∆p = ρg∆h
  • use the equation ∆p = ρg∆h
  • understand that the upthrust acting on an object in a fluid is due to a difference in hydrostatic pressure
  • calculate the upthrust acting on an object in a fluid using the equation F = ρgV (Archimedes’ principle)

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Chapter 4: Density and pressure

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119 questions

1May / June 2026 · Paper 11 · Q14
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AIt is proportional to the density of the liquid.
BIt is proportional to the density of the object.
CIt is proportional to the total depth of the liquid.
DIt is proportional to the weight of the object.

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2May / June 2026 · Paper 12 · Q13
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Aadding more liquid into the cylinder
Bdecreasing the density of the liquid
Cincreasing the air pressure above the liquid
Dincreasing the density of the liquid

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3May / June 2026 · Paper 12 · Q15
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A0.5 g
B5 g
C50 g
D500 g

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4May / June 2026 · Paper 13 · Q13
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Aobject of volume V fully submerged near the bottom of the beaker
Bobject of volume 2V fully submerged near the bottom of the beaker
Cobject of volume V floating at the surface of the beaker
Dobject of volume 2V floating at the surface of the beaker

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5May / June 2026 · Paper 13 · Q14
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A4.5 cm
B6.2 cm
C23.8 cm
D25.5 cm

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6May / June 2026 · Paper 13 · Q15
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A$\frac{1}{3}\rho r^2$
B$\frac{1}{3}\rho r^2 g$
C$\frac{2}{3}\rho r$
D$\frac{2}{3}\rho r g$

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7May / June 2026 · Paper 14 · Q13
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Aequal to volume of water displaced | not equal at all points
Bequal to volume of water displaced | equal at all points
Cequal to weight of water displaced | not equal at all points
Dequal to weight of water displaced | equal at all points

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8May / June 2026 · Paper 14 · Q15
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A79 kg
B190 kg
C790 kg
D1900 kg

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9Oct / Nov 2025 · Paper 11 · Q15
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A1 × 10⁰ Pa
B1 × 10² Pa
C1 × 10⁴ Pa
D1 × 10⁶ Pa

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10Oct / Nov 2025 · Paper 11 · Q16
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Adensity of water; volume of whole block
Bdensity of water; volume of block below surface of water
Cdensity of wood; volume of whole block
Ddensity of wood; volume of block below surface of water

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11Oct / Nov 2025 · Paper 12 · Q15
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Adecrease mass, decrease volume
Bdecrease mass, increase volume
Cincrease mass, decrease volume
Dincrease mass, increase volume

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12Oct / Nov 2025 · Paper 12 · Q16
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A0.38
B1.0
C2.7
D3.6

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13Oct / Nov 2025 · Paper 13 · Q15
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A1 × 10⁰ Pa
B1 × 10² Pa
C1 × 10⁴ Pa
D1 × 10⁶ Pa

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14Oct / Nov 2025 · Paper 13 · Q16
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Adensity of water | volume of whole block
Bdensity of water | volume of block below surface of water
Cdensity of wood | volume of whole block
Ddensity of wood | volume of block below surface of water

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15Oct / Nov 2025 · Paper 14 · Q9
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AIt is proportional to the acceleration of free fall.
BIt is equal to the weight of the sphere.
CIt is proportional to the density of the sphere.
DIt is proportional to the square of the radius of the sphere.

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16Oct / Nov 2025 · Paper 14 · Q12
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A$P_A + \frac{4}{3}\pi r^3 \rho g$
B$P_A - \frac{4}{3}\pi r^3 \rho g$
C$2r\rho g + P_A$
D$2r\rho g - P_A$

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17May / June 2025 · Paper 11 · Q14
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A8.5 N
B9.0 N
C11.0 N
D11.5 N

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18May / June 2025 · Paper 11 · Q16
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A0
B0.5p
Cp
D2p

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19May / June 2025 · Paper 12 · Q14
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AρgV
Bmg + ρgV
Cmg
DρgV − mg

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20May / June 2025 · Paper 12 · Q16
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ADiagram A
BDiagram B
CDiagram C
DDiagram D

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21May / June 2025 · Paper 13 · Q13
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Amass of one cubic metre
Bmass of a unit volume
Cmass per cubic metre
Dmass per unit volume

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22May / June 2025 · Paper 13 · Q15
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A1200 Pa
B1600 Pa
C3600 Pa
D4800 Pa

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23May / June 2025 · Paper 14 · Q12
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A11 kPa
B26 kPa
C53 kPa
D110 kPa

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24May / June 2025 · Paper 14 · Q13
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A\left(1 - \dfrac{\rho_i}{\rho_w}\right) H
B\left(\dfrac{\rho_i}{\rho_w} - 1\right) H
C\dfrac{\rho_w}{\rho_i} H
D\dfrac{\rho_i}{\rho_w} H

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25Feb / March 2025 · Paper 12 · Q10
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AUse a different liquid that has twice the density and the same volume as the original liquid.
BUse a different object that has half the volume and the same density as the original object.
CUse a different object that has twice the density and the same volume as the original object.
DUse a different object that has twice the volume and the same density as the original object.

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26Oct / Nov 2024 · Paper 11 · Q15
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Aupthrust on the sphere: constant; resultant force on the sphere: decreasing
Bupthrust on the sphere: constant; resultant force on the sphere: increasing
Cupthrust on the sphere: decreasing; resultant force on the sphere: decreasing
Dupthrust on the sphere: decreasing; resultant force on the sphere: increasing

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27Oct / Nov 2024 · Paper 12 · Q14
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A1.13 kPa
B1.70 kPa
C11.1 kPa
D16.6 kPa

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28Oct / Nov 2024 · Paper 13 · Q5
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AThe upthrust of the water on each of the cuboids is the same.
BThe upthrust of the water on W is twice the upthrust of the water on X.
CThe upthrust of the water on X is twice the upthrust of the water on W.
DThe upthrust of the water on Y is zero.

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29Oct / Nov 2024 · Paper 13 · Q16
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A\frac{1}{2}
B\frac{2}{3}
C\frac{3}{2}
D2

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30May / June 2024 · Paper 11 · Q11
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A0.88 m
B1.1 m
C1.8 m
D8.7 m

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31May / June 2024 · Paper 12 · Q13
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A4.0 cm³
B8.0 cm³
C34 cm³
D80 cm³

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32May / June 2024 · Paper 13 · Q13
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A3.8 × 10⁻²⁹ m
B6.2 × 10⁻¹⁵ m
C3.4 × 10⁻¹⁰ m
D3.0 × 10⁻⁹ m

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33May / June 2024 · Paper 13 · Q14
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AA
BB
CC
DD

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34Feb / March 2024 · Paper 12 · Q10
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AThe drag force increases with increasing depth.
BThe drag force is equal to the sum of the upthrust and weight.
CThe upthrust is constant with increasing depth.
DThe weight is greater than the sum of the drag force and the upthrust.

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35Feb / March 2024 · Paper 12 · Q11
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A0.39 kN
B0.39 MN
C0.63 MN
D0.63 GN

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36Feb / March 2024 · Paper 12 · Q12
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A907 m
B1000 m
C1090 m
D1270 m

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37Oct / Nov 2023 · Paper 11 · Q14
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A$\dfrac{W-P}{Q-P}$
B$\dfrac{Q-P}{W-P}$
C$\dfrac{W-P}{W-Q}$
D$\dfrac{W-Q}{W-P}$

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38Oct / Nov 2023 · Paper 12 · Q14
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AThe force due to the liquid acting on the top surface of X is greater than that acting on the top surface of Y.
BThe pressure difference due to the liquid between the top and bottom surfaces of X is the same as that for Y.
CThe upthrust acting on X is the same as the upthrust acting on Y.
DThe weight of X is the same as the weight of Y.

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39Oct / Nov 2023 · Paper 13 · Q13
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A1.25 × 10² kg m⁻³
B9.15 × 10² kg m⁻³
C9.28 × 10² kg m⁻³
D1.16 × 10³ kg m⁻³

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40Oct / Nov 2023 · Paper 13 · Q14
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Aforce per unit area
Bmass per unit area
Cmass per unit volume
Dweight per unit volume

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41May / June 2023 · Paper 11 · Q14
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Aforce per unit area
Bforce per unit volume
Cmass per unit area
Dmass per unit volume

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42May / June 2023 · Paper 11 · Q15
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A3.9%
B38%
C62%
D96%

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43May / June 2023 · Paper 12 · Q1
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A8 × 10² kg m⁻³
B2 × 10³ kg m⁻³
C8 × 10³ N m⁻³
D2 × 10⁴ N m⁻³

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44May / June 2023 · Paper 12 · Q13
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A1.26
B1.41
C2.00
D8.00

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45May / June 2023 · Paper 12 · Q14
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A780 Pa
B1200 Pa
C1600 Pa
D2000 Pa

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46May / June 2023 · Paper 13 · Q13
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A850 kg m⁻³
B900 kg m⁻³
C940 kg m⁻³
D950 kg m⁻³

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47May / June 2023 · Paper 13 · Q14
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AFU = WL
BFU = WO – WL
CFU = WO
DFU = WO + WL

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48Feb / March 2023 · Paper 12 · Q13
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A1/3 ρr²
B1/3 ρr²g
C2/3 ρr
D2/3 ρrg

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49Feb / March 2023 · Paper 12 · Q14
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A1.98 × 10^-4 m^3
B2.97 × 10^-4 m^3
C4.95 × 10^-4 m^3
D6.93 × 10^-4 m^3

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50Oct / Nov 2022 · Paper 11 · Q14
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A40 cm³
B44 cm³
C52 cm³
D80 cm³

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51Oct / Nov 2022 · Paper 11 · Q15
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AGraph A: upthrust increases linearly from origin with depth
BGraph B: upthrust constant from origin with depth
CGraph C: upthrust increases linearly then becomes constant
DGraph D: upthrust increases with decreasing gradient then becomes constant

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52Oct / Nov 2022 · Paper 12 · Q15
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A3300 kg m⁻³
B4600 kg m⁻³
C14 000 kg m⁻³
D19 000 kg m⁻³

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53Oct / Nov 2022 · Paper 12 · Q16
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A2/1
B√2/1
C1/√2
D1/2

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54Oct / Nov 2022 · Paper 13 · Q14
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A6.4 m s–1
B13 m s–1
C25 m s–1
D51 m s–1

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55Oct / Nov 2022 · Paper 13 · Q15
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Athe product of the acceleration of free fall and the density of the cube
Bthe product of the acceleration of free fall, the density and the side length of the cube
Cthe product of the acceleration of free fall, the density and the area of one face of the cube
Dthe product of the acceleration of free fall, the density and the volume of the cube

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56May / June 2022 · Paper 11 · Q14
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AU/4
BU
C2U
D4U

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57May / June 2022 · Paper 11 · Q15
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A927 kg m⁻³
B933 kg m⁻³
C957 kg m⁻³
D1045 kg m⁻³

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58May / June 2022 · Paper 12 · Q14
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A0.5ρ
Bρ
C2ρ
D4ρ

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59May / June 2022 · Paper 12 · Q15
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Ap₁ = ρgy
Bp₂ = ρg(x − z)
Cp₁ − p₂ = ρg(y − z)
Dp₁ + p₂ = ρgx

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60May / June 2022 · Paper 13 · Q15
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Aρ_L a³ g
Bρ_w a³ g
Cρ_L h g
Dρ_L a g

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61Feb / March 2022 · Paper 12 · Q13
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AThe sphere always moves with constant acceleration.
BThe sphere always moves with constant velocity.
CThe upthrust on the sphere always decreases.
DThe upthrust on the sphere is always constant.

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62Oct / Nov 2021 · Paper 11 · Q11
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Adecrease the density of the block
Bhold the block horizontally
Cincrease dimension y
Dincrease the density of the block

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63Oct / Nov 2021 · Paper 11 · Q14
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A14.7 kPa
B86.3 kPa
C103 kPa
D116 kPa

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64Oct / Nov 2021 · Paper 12 · Q11
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A(p_b − p_t)
B(p_b − p_t)A
C(p_b − p_t)A − W
D(p_b − p_t)A + W

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65Oct / Nov 2021 · Paper 12 · Q15
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AGraph A
BGraph B
CGraph C
DGraph D

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66Oct / Nov 2021 · Paper 13 · Q15
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A1/2 U
BU
C2U
D4U

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67May / June 2021 · Paper 11 · Q14
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A390 Pa
B880 Pa
C1200 Pa
D1300 Pa

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68May / June 2021 · Paper 12 · Q14
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A8.7 kPa
B35 kPa
C85 kPa
D340 kPa

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69May / June 2021 · Paper 13 · Q15
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Adensity = mass/volume
Bpotential energy = mass × acceleration of free fall × height
Cpressure = force/area
Dweight = mass × acceleration of free fall

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70Feb / March 2021 · Paper 12 · Q14
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A\frac{G}{2\pi r}
BG2\pi r
C\frac{G}{\pi r^2}
DG\pi r^2

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71Oct / Nov 2020 · Paper 11 · Q14
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A99 kPa
B100 kPa
C102 kPa
D103 kPa

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72Oct / Nov 2020 · Paper 12 · Q15
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A3.3 mm
B3.3 cm
C0.32 m
D3.1 m

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73Oct / Nov 2020 · Paper 13 · Q15
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Aρ_C A H g
Bρ_C A X g
Cρ_L A H g
Dρ_L A X g

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74May / June 2020 · Paper 11 · Q15
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A190 kg m–3
B1900 kg m–3
C19 000 kg m–3
D190 000 kg m–3

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75May / June 2020 · Paper 12 · Q13
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A680 kg m^-3
B910 kg m^-3
C6700 kg m^-3
D8900 kg m^-3

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76May / June 2020 · Paper 13 · Q2
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A4.0 × 10⁻³ kg m⁻³
B4.0 × 10⁻⁵ kg m⁻³
C4.0 × 10⁻⁶ kg m⁻³
D4.0 × 10⁻⁸ kg m⁻³

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77May / June 2020 · Paper 13 · Q11
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AThe air in the submarine is less dense than sea water.
BThere is a difference in water pressure acting on the top and on the bottom of the submarine.
CThe sea water exerts a greater upward force on the submarine than the weight of the steel.
DThe submarine displaces its own volume of sea water.

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78May / June 2020 · Paper 13 · Q15
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A\frac{2x}{7}
B\frac{7x}{8}
C\frac{8x}{7}
D\frac{7x}{2}

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79Oct / Nov 2019 · Paper 11 · Q11
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A$\dfrac{W-P}{Q-P}$
B$\dfrac{Q-P}{W-P}$
C$\dfrac{W-P}{W-Q}$
D$\dfrac{W-Q}{W-P}$

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80Oct / Nov 2019 · Paper 11 · Q14
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A927 kg m–3
B933 kg m–3
C957 kg m–3
D1045 kg m–3

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81Oct / Nov 2019 · Paper 12 · Q13
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AA
BB
CC
DD

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82Oct / Nov 2019 · Paper 13 · Q10
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Aupthrust on the sphere: constant; resultant force on the sphere: increasing
Bupthrust on the sphere: constant; resultant force on the sphere: decreasing
Cupthrust on the sphere: decreasing; resultant force on the sphere: increasing
Dupthrust on the sphere: decreasing; resultant force on the sphere: decreasing

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83Oct / Nov 2019 · Paper 13 · Q13
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A7.8 km
B16 km
C77 km
D150 km

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84May / June 2019 · Paper 11 · Q12
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A\left(1 - \dfrac{\rho_i}{\rho_w}\right) H
B\left(\dfrac{\rho_i}{\rho_w} - 1\right) H
C\dfrac{\rho_w}{\rho_i} H
D\dfrac{\rho_i}{\rho_w} H

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85May / June 2019 · Paper 11 · Q16
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A0.961 g cm–3
B0.972 g cm–3
C1.03 g cm–3
D1.04 g cm–3

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86May / June 2019 · Paper 12 · Q15
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A850 kg m⁻³
B900 kg m⁻³
C940 kg m⁻³
D950 kg m⁻³

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87May / June 2019 · Paper 12 · Q21
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A3.8 × 10⁻²⁹ m
B6.2 × 10⁻¹⁵ m
C3.4 × 10⁻¹⁰ m
D3.0 × 10⁻⁹ m

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88May / June 2019 · Paper 13 · Q14
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A4.0 cm3
B8.0 cm3
C34 cm3
D80 cm3

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89Feb / March 2019 · Paper 12 · Q11
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AThe drag-force increases with increasing depth.
BThe drag-force is equal to the sum of the upthrust and weight.
CThe upthrust is constant with increasing depth.
DThe weight is greater than the sum of the drag-force and the upthrust.

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90Feb / March 2019 · Paper 12 · Q14
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A\frac{1}{3} ρr^2
B\frac{1}{3} ρr^2g
C\frac{2}{3} ρr
D\frac{2}{3} ρrg

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91Oct / Nov 2018 · Paper 11 · Q13
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A1960 Pa
B2940 Pa
C4910 Pa
D7850 Pa

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92Oct / Nov 2018 · Paper 12 · Q14
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Agraph A
Bgraph B
Cgraph C
Dgraph D

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93May / June 2018 · Paper 11 · Q11
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AP and T
BQ and R
CQ and S
DS and T

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94May / June 2018 · Paper 11 · Q13
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A8, 20
B10, 15
C15, 10
D20, 8

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95May / June 2018 · Paper 12 · Q10
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A40 cm³
B44 cm³
C52 cm³
D80 cm³

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96May / June 2018 · Paper 12 · Q12
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A(p_b – pₜ)
B(p_b – pₜ)A
C(p_b – pₜ)A – W
D(p_b – pₜ)A + W

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97May / June 2018 · Paper 13 · Q10
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AThe upthrust of the water on each of the cuboids is the same.
BThe upthrust of the water on W is twice the upthrust of the water on X.
CThe upthrust of the water on X is twice the upthrust of the water on W.
DThe upthrust of the water on Y is zero.

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98May / June 2018 · Paper 13 · Q11
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A1.13 kPa
B1.70 kPa
C11.1 kPa
D16.6 kPa

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99May / June 2018 · Paper 13 · Q13
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A1.25 × 10^2 kg m^-3
B9.15 × 10^2 kg m^-3
C9.28 × 10^2 kg m^-3
D1.16 × 10^3 kg m^-3

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100Feb / March 2018 · Paper 12 · Q4
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A0.5 g
B5 g
C50 g
D500 g

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101Oct / Nov 2017 · Paper 11 · Q12
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ADiagram A
BDiagram B
CDiagram C
DDiagram D

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102Oct / Nov 2017 · Paper 11 · Q15
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Adensity = mass/volume
Bpotential energy = mass × acceleration of free fall × height
Cpressure = force/area
Dweight = mass × acceleration of free fall

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103Oct / Nov 2017 · Paper 12 · Q11
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ACopper is more dense than water.
BThe area of face R is greater than the area of face S.
CThe density of water increases with depth.
DThe pressure of water increases with depth.

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104Oct / Nov 2017 · Paper 12 · Q15
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AP + gρwhw + gρmhm
BP + gρwhw – gρmhm
Cgρwhw + gρmhm
Dgρwhw – gρmhm

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105Oct / Nov 2017 · Paper 13 · Q14
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A0.88 m
B1.1 m
C1.8 m
D8.7 m

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106May / June 2017 · Paper 11 · Q14
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A2.5 g cm⁻³
B4.6 g cm⁻³
C5.4 g cm⁻³
D10.7 g cm⁻³

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107May / June 2017 · Paper 12 · Q10
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AAt P and at Q, the tension T in the cord is the same because the difference in pressure between the top and bottom of the cylinder is the same.
BAt Q, the tension T in the cord is less than at P because, at smaller depth, liquid pressure is smaller.
CAt R, the tension T in the cord is less than at P because atmospheric pressure is less than water pressure.
DAt S, the tension T in the cord is greater than at P because atmospheric pressure at S exerts no force on the top or bottom of the cylinder.

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108May / June 2017 · Paper 13 · Q13
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AP < R and S = Q
BP > R and S = Q
CP = R and S = Q and P < S
DP = R and S = Q and P = S

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109Feb / March 2017 · Paper 12 · Q15
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Afriction
Bupthrust
Cviscous force
Dweight

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110Oct / Nov 2016 · Paper 11 · Q14
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A47 000 N
B190 000 N
C310 000 N
D620 000 N

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111Oct / Nov 2016 · Paper 12 · Q1
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A79 kg
B190 kg
C790 kg
D1900 kg

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112Oct / Nov 2016 · Paper 12 · Q16
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A300 N
B530 N
C1200 N
D4800 N

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113Oct / Nov 2016 · Paper 13 · Q14
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A47 000 N
B190 000 N
C310 000 N
D620 000 N

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114May / June 2016 · Paper 11 · Q13
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A\frac{p}{gx}
B\frac{gx}{p}
C\frac{pA}{gx}
D\frac{gx}{pA}

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115May / June 2016 · Paper 11 · Q15
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A965 kg m^{-3}
B1340 kg m^{-3}
C7720 kg m^{-3}
D10 700 kg m^{-3}

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116May / June 2016 · Paper 12 · Q13
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A927 kg m⁻³
B957 kg m⁻³
C1010 kg m⁻³
D1080 kg m⁻³

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117May / June 2016 · Paper 12 · Q15
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A36 000 Pa
B48 000 Pa
C52 000 Pa
D59 000 Pa

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118May / June 2016 · Paper 13 · Q15
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Aatmospheric pressure decreases with height
Bchange in gravitational potential energy = mass × gΔh
Cρ = mass / volume
Dthe density of a fluid increases with depth

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119Feb / March 2016 · Paper 12 · Q14
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A82 000 Pa
B206 000 Pa
C288 000 Pa
D389 000 Pa

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