Equilibrium of forces
4.2What the syllabus asks of you
- state and apply the principle of moments
- understand that, when there is no resultant force and no resultant torque, a system is in equilibrium
- use a vector triangle to represent coplanar forces in equilibrium
Read the notes first
Chapter 4: Equilibrium of forces
Drill this topic
Every question on Equilibrium of forces, untimed, marked as you go.
Make a worksheet
Choose the years and how many questions, then print it with the answers on separate pages.
104 questions
1May / June 2026 · Paper 11 · Q15Show mark scheme →
A1/4
B1/2
C1
D2
Mark scheme
2May / June 2026 · Paper 12 · Q3Show mark scheme →
A% increase in magnitude of Q: 10; % increase in magnitude of R: 10
B% increase in magnitude of Q: 0; % increase in magnitude of R: 10
C% increase in magnitude of Q: 10\sqrt{2}; % increase in magnitude of R: 10\sqrt{2}
D% increase in magnitude of Q: 10; % increase in magnitude of R: 10\sqrt{2}
Mark scheme
3May / June 2026 · Paper 12 · Q16Show mark scheme →
AIf a system is in equilibrium then there must be no forces acting on it.
BIf a system is in equilibrium then there must be no resultant torque on it.
CIf there are no moments due to forces acting on a system then it must be in equilibrium.
DIf there is no resultant force acting on a system then it must be in equilibrium.
Mark scheme
4May / June 2026 · Paper 13 · Q8Show mark scheme →
Aacceleration
Bdisplacement
Cmomentum
Dvelocity
Mark scheme
5May / June 2026 · Paper 13 · Q12Show mark scheme →
Aresultant force: zero; resultant torque: zero
Bresultant force: zero; resultant torque: not zero
Cresultant force: not zero; resultant torque: zero
Dresultant force: not zero; resultant torque: not zero
Mark scheme
6May / June 2026 · Paper 14 · Q12Show mark scheme →
AThe acceleration of the object must be zero.
BThe resultant force acting on the object must be zero.
CThe resultant moment of any two forces about the point of action of the third force must be zero.
DThe velocity of the object must be zero.
Mark scheme
7Oct / Nov 2025 · Paper 12 · Q14Show mark scheme →
A\frac{xM}{m}
B\frac{M}{m}(L - x)
C\frac{M}{2m}(L - 2x)
D\frac{1}{m}(Lm - xM)
Mark scheme
8Oct / Nov 2025 · Paper 14 · Q13Show mark scheme →
Aupward arrow
Bdownward arrow
Carrow pointing up-left
Darrow pointing up-right
Mark scheme
9Oct / Nov 2025 · Paper 14 · Q15Show mark scheme →
A310 N
B450 N
C590 N
D900 N
Mark scheme
10May / June 2025 · Paper 11 · Q15Show mark scheme →
A30 g
B40 g
C47 g
D133 g
Mark scheme
11May / June 2025 · Paper 13 · Q10Show mark scheme →
AIt is accelerating.
BIt is moving in a straight line.
CIt is moving with decreasing speed.
DIt is moving with increasing momentum.
Mark scheme
12May / June 2025 · Paper 13 · Q12Show mark scheme →
A0.050 m
B0.10 m
C0.25 m
D0.40 m
Mark scheme
13May / June 2025 · Paper 13 · Q14Show mark scheme →
Avector triangle A
Bvector triangle B
Cvector triangle C
Dvector triangle D
Mark scheme
14May / June 2025 · Paper 14 · Q11Show mark scheme →
A
B
C
D
Mark scheme
15Feb / March 2025 · Paper 12 · Q11Show mark scheme →
A0 N
B43 N
C130 N
D150 N
Mark scheme
16Feb / March 2025 · Paper 12 · Q13Show mark scheme →
A600, 0
B600, 150
C750, 0
D750, 150
Mark scheme
17Oct / Nov 2024 · Paper 11 · Q8Show mark scheme →
ADiagram A
BDiagram B
CDiagram C
DDiagram D
Mark scheme
18Oct / Nov 2024 · Paper 11 · Q16Show mark scheme →
A140 N
B170 N
C200 N
D400 N
Mark scheme
19Oct / Nov 2024 · Paper 12 · Q11Show mark scheme →
AThe object has a constant non-zero acceleration.
BThe object is stationary.
CThere are no forces acting on the object.
DThe resultant force acting on the object is zero.
Mark scheme
20Oct / Nov 2024 · Paper 12 · Q12Show mark scheme →
AVector diagram A
BVector diagram B
CVector diagram C
DVector diagram D
Mark scheme
21Oct / Nov 2024 · Paper 13 · Q6Show mark scheme →
AAn aeroplane climbs at a steady rate.
BAn aeroplane tows a glider at a constant altitude.
CA speedboat changes direction at a constant speed.
DTwo boats tow a ship into harbour.
Mark scheme
22Oct / Nov 2024 · Paper 13 · Q14Show mark scheme →
A0.010 N m
B0.10 N m
C0.29 N m
D2.8 N m
Mark scheme
23Oct / Nov 2024 · Paper 13 · Q15Show mark scheme →
AP and Q
BP and R
CQ and R
Dnone of them
Mark scheme
24May / June 2024 · Paper 11 · Q14Show mark scheme →
ADiagram A
BDiagram B
CDiagram C
DDiagram D
Mark scheme
25May / June 2024 · Paper 12 · Q12Show mark scheme →
A0.87 N
B1.5 N
C2.6 N
D5.2 N
Mark scheme
26May / June 2024 · Paper 13 · Q11Show mark scheme →
A36 N at 157°
B36 N at 157°
C55 N at 165°
D55 N at 165°
Mark scheme
27May / June 2024 · Paper 13 · Q12Show mark scheme →
A1 and 2 only
B1 and 3 only
C2 and 3 only
D1, 2 and 3
Mark scheme
28Feb / March 2024 · Paper 12 · Q14Show mark scheme →
AH, T, W
BT, H, W
CW, H, T
DW, T, H
Mark scheme
29Feb / March 2024 · Paper 12 · Q17Show mark scheme →
AThe disc is in equilibrium because the resultant force is zero.
BThe disc is not in equilibrium because the resultant force is 4F.
CThe disc is in equilibrium because the resultant torque is zero.
DThe disc is not in equilibrium because the resultant torque is 2Fd.
Mark scheme
30Oct / Nov 2023 · Paper 11 · Q12Show mark scheme →
A3/2
B2/3
C3/5
D2/5
Mark scheme
31Oct / Nov 2023 · Paper 11 · Q13Show mark scheme →
AThe firework is in equilibrium because the resultant force acting on it is zero.
BThe firework is in equilibrium because the resultant torque acting on it is zero.
CThe firework is not in equilibrium because the resultant force acting on it is not zero.
DThe firework is not in equilibrium because the resultant torque acting on it is not zero.
Mark scheme
32Oct / Nov 2023 · Paper 12 · Q4Show mark scheme →
AL = W cos θ and T = R + W sin θ
BL = W sin θ and T = R + W cos θ
CL = W cos θ and T = R – W sin θ
DL = W sin θ and T = R – W cos θ
Mark scheme
33Oct / Nov 2023 · Paper 12 · Q13Show mark scheme →
A0.075 N
B0.087 N
C0.26 N
D0.30 N
Mark scheme
34Oct / Nov 2023 · Paper 13 · Q12Show mark scheme →
A130 N
B160 N
C260 N
D310 N
Mark scheme
35May / June 2023 · Paper 11 · Q13Show mark scheme →
AP = T cosθ and W = T sinθ
BT = P + W
CT² = P² + W²
DW = P tanθ and W = T cosθ
Mark scheme
36May / June 2023 · Paper 12 · Q12Show mark scheme →
A5.0 N
B8.7 N
C10 N
D20 N
Mark scheme
37May / June 2023 · Paper 13 · Q12Show mark scheme →
A38 g
B44 g
C120 g
D136 g
Mark scheme
38Feb / March 2023 · Paper 12 · Q12Show mark scheme →
AR1 = R2 T1 = T2
BR1 = R2 T1 > T2
CR1 > R2 T1 < T2
DR1 < R2 T1 = T2
Mark scheme
39Oct / Nov 2022 · Paper 11 · Q12Show mark scheme →
ADiagram A: upward forces ½F at each end, downward force F at centre
BDiagram B: upward forces F at centre and right, downward force F at left
CDiagram C: upward forces F at each end, downward force F at centre
DDiagram D: upward forces ½F at each end, downward forces ½F at each end
Mark scheme
40Oct / Nov 2022 · Paper 11 · Q13Show mark scheme →
A3.7 N
B33 N
C36 N
D320 N
Mark scheme
41Oct / Nov 2022 · Paper 12 · Q13Show mark scheme →
A0.066 kg
B0.13 kg
C0.22 kg
D1.3 kg
Mark scheme
42Oct / Nov 2022 · Paper 12 · Q14Show mark scheme →
A40 kg
B42 kg
C390 kg
D410 kg
Mark scheme
43Oct / Nov 2022 · Paper 13 · Q12Show mark scheme →
AEither X or Y is the centre of gravity of the object.
BEither X or Y is the pivot of the object.
CX and Y are at opposite ends of the object.
DX and Y are the same point on the object.
Mark scheme
44Oct / Nov 2022 · Paper 13 · Q13Show mark scheme →
A3.4 N
B4.0 N
C6.8 N
D8.1 N
Mark scheme
45May / June 2022 · Paper 11 · Q12Show mark scheme →
Awhen no resultant force acts on the object
Bwhen no resultant force and no resultant torque act on the object
Cwhen no resultant torque acts on the object
Dwhen the upward force on the object is equal and opposite to its weight
Mark scheme
46May / June 2022 · Paper 11 · Q13Show mark scheme →
Aforce at P decreases, force at Q decreases
Bforce at P decreases, force at Q increases
Cforce at P increases, force at Q decreases
Dforce at P increases, force at Q increases
Mark scheme
47May / June 2022 · Paper 12 · Q12Show mark scheme →
Aupward arrow
Bdownward arrow
Carrow pointing up-left
Darrow pointing up-right
Mark scheme
48May / June 2022 · Paper 12 · Q13Show mark scheme →
A1.0 cm
B1.6 cm
C9.8 cm
D16 cm
Mark scheme
49May / June 2022 · Paper 13 · Q13Show mark scheme →
A
B
C
D
Mark scheme
50May / June 2022 · Paper 13 · Q14Show mark scheme →
A333 g
B500 g
C667 g
D1000 g
Mark scheme
51Feb / March 2022 · Paper 12 · Q12Show mark scheme →
AIt must be somewhere along a horizontal line that is 0.5 cm from line WX.
BIt must be somewhere along a horizontal line that is 0.5 cm from line YZ.
CIt must be somewhere along a vertical line that is 0.5 cm from line WY.
DIt must be somewhere along a vertical line that is 0.5 cm from line XZ.
Mark scheme
52Oct / Nov 2021 · Paper 11 · Q13Show mark scheme →
Aany point
Bthe centre of gravity of the object
Cthe pivot
Dthe same point
Mark scheme
53Oct / Nov 2021 · Paper 12 · Q14Show mark scheme →
A4.0 kN
B4.6 kN
C6.9 kN
D8.0 kN
Mark scheme
54Oct / Nov 2021 · Paper 13 · Q14Show mark scheme →
A30 N
B60 N
C80 N
D140 N
Mark scheme
55May / June 2021 · Paper 12 · Q13Show mark scheme →
A11°
B22°
C68°
D79°
Mark scheme
56Feb / March 2021 · Paper 12 · Q13Show mark scheme →
A17 N
B150 N
C170 N
D510 N
Mark scheme
57Oct / Nov 2020 · Paper 11 · Q13Show mark scheme →
ADiagram A
BDiagram B
CDiagram C
DDiagram D
Mark scheme
58Oct / Nov 2020 · Paper 12 · Q13Show mark scheme →
A25 N
B50 N
C75 N
D100 N
Mark scheme
59Oct / Nov 2020 · Paper 12 · Q14Show mark scheme →
A0.44 kN
B0.89 kN
C1.2 kN
D2.4 kN
Mark scheme
60Oct / Nov 2020 · Paper 13 · Q13Show mark scheme →
Ahorizontal component: F cos θ; vertical component: (W_s + W_b – F cos θ)
Bhorizontal component: F cos θ; vertical component: (W_s + W_b – F sin θ)
Chorizontal component: F sin θ; vertical component: (W_s + W_b – F cos θ)
Dhorizontal component: F sin θ; vertical component: (W_s + W_b – F sin θ)
Mark scheme
61Oct / Nov 2020 · Paper 13 · Q14Show mark scheme →
A
B
C
D
Mark scheme
62May / June 2020 · Paper 11 · Q11Show mark scheme →
Africtional force on block: down the board; resultant force on block: down the board
Bfrictional force on block: down the board; resultant force on block: zero
Cfrictional force on block: up the board; resultant force on block: down the board
Dfrictional force on block: up the board; resultant force on block: zero
Mark scheme
63May / June 2020 · Paper 11 · Q13Show mark scheme →
A5.0 N
B8.7 N
C10.0 N
D20.0 N
Mark scheme
64May / June 2020 · Paper 11 · Q14Show mark scheme →
Atriangle of vectors forming a closed loop
Bthree vectors not forming a closed loop
Cthree vectors not forming a closed loop
Dthree vectors not forming a closed loop
Mark scheme
65May / June 2020 · Paper 12 · Q12Show mark scheme →
AVector triangle A
BVector triangle B
CVector triangle C
DVector triangle D
Mark scheme
66May / June 2020 · Paper 13 · Q13Show mark scheme →
A10 cm
B15 cm
C25 cm
D40 cm
Mark scheme
67May / June 2020 · Paper 13 · Q14Show mark scheme →
Aarrow pointing up-right
Barrow pointing down-left
Carrow pointing left
Darrow pointing down-right
Mark scheme
68Feb / March 2020 · Paper 12 · Q13Show mark scheme →
ADiagram A
BDiagram B
CDiagram C
DDiagram D
Mark scheme
69Oct / Nov 2019 · Paper 11 · Q13Show mark scheme →
A41 N
B77 N
C113 N
D128 N
Mark scheme
70Oct / Nov 2019 · Paper 13 · Q12Show mark scheme →
Atension in cable, weight of ball, tension in chain (diagram A)
Btension in cable, weight of ball, tension in chain (diagram B)
Ctension in cable, weight of ball, tension in chain (diagram C)
Dtension in cable, weight of ball, tension in chain (diagram D)
Mark scheme
71May / June 2019 · Paper 11 · Q14Show mark scheme →
A0.0408 m
B0.240 m
C4.16 m
D40.8 m
Mark scheme
72May / June 2019 · Paper 11 · Q15Show mark scheme →
AThey all act along the same line.
BThey all have the same magnitude.
CThey do not all act along the same line.
DThey do not all have the same magnitude.
Mark scheme
73May / June 2019 · Paper 12 · Q12Show mark scheme →
Aweight < drag
Bweight = drag
Cweight < upthrust
Dweight > upthrust
Mark scheme
74May / June 2019 · Paper 12 · Q14Show mark scheme →
Amg cos θ
Bmg sin θ
Cmg cos θ + F
Dmg sin θ + F
Mark scheme
75May / June 2019 · Paper 13 · Q11Show mark scheme →
AIncreasing the length of the cord, with points X and Y in the same place on the picture, would reduce the tension in the cord.
BMoving points X and Y further apart on the picture while keeping the length of the cord constant would reduce the tension in the cord.
CMoving points X and Y to the top edge of the picture while keeping their distance apart constant and the length of the cord constant would reduce the tension in the cord.
DThe weight of the picture is equal to T cosθ.
Mark scheme
76May / June 2019 · Paper 13 · Q12Show mark scheme →
A0 N
B43 N
C130 N
D150 N
Mark scheme
77Feb / March 2019 · Paper 12 · Q13Show mark scheme →
A50 N
B58 N
C86 N
D100 N
Mark scheme
78Oct / Nov 2018 · Paper 11 · Q11Show mark scheme →
A30 N
B60 N
C80 N
D140 N
Mark scheme
79Oct / Nov 2018 · Paper 11 · Q12Show mark scheme →
AVector triangle with P pointing down-left, W pointing down, Q pointing up-right
BVector triangle with P pointing down-left, Q pointing up-right, W pointing down
CVector triangle with P pointing up-right, W pointing down, Q pointing up-right
DVector triangle with P pointing down-left, W pointing up, Q pointing down
Mark scheme
80Oct / Nov 2018 · Paper 12 · Q12Show mark scheme →
A160 cm²
B320 cm²
C640 cm²
D1600 cm²
Mark scheme
81Oct / Nov 2018 · Paper 12 · Q13Show mark scheme →
AT, F, W vector diagram
BT, F, W vector diagram
CT, F, W vector diagram
DF, T, W vector diagram
Mark scheme
82Oct / Nov 2018 · Paper 13 · Q13Show mark scheme →
A1000 N
B1500 N
C2100 N
D3000 N
Mark scheme
83May / June 2018 · Paper 12 · Q13Show mark scheme →
Adecreases / decreases
Bdecreases / increases
Cincreases / decreases
Dincreases / increases
Mark scheme
84May / June 2018 · Paper 12 · Q17Show mark scheme →
AP = T cosθ and W = T sinθ
BT = P + W
CT² = P² + W²
DW = P tanθ and W = T cosθ
Mark scheme
85Feb / March 2018 · Paper 12 · Q13Show mark scheme →
AAn aeroplane climbs at a steady rate.
BAn aeroplane tows a glider at a constant altitude.
CA speedboat changes direction at a constant speed.
DTwo boats tow a ship into harbour.
Mark scheme
86Oct / Nov 2017 · Paper 11 · Q8Show mark scheme →
AF
B2F
C3F
D4F
Mark scheme
87Oct / Nov 2017 · Paper 11 · Q14Show mark scheme →
A60 mm backwards
B60 mm forwards
C140 mm backwards
D140 mm forwards
Mark scheme
88Oct / Nov 2017 · Paper 12 · Q13Show mark scheme →
A
B
C
D
Mark scheme
89Oct / Nov 2017 · Paper 12 · Q14Show mark scheme →
A2.6 × 10⁴ N
B3.1 × 10⁴ N
C5.2 × 10⁴ N
D6.2 × 10⁴ N
Mark scheme
90May / June 2017 · Paper 11 · Q13Show mark scheme →
A2200 N
B2300 N
C2400 N
D2600 N
Mark scheme
91May / June 2017 · Paper 12 · Q12Show mark scheme →
AA
BB
CC
DD
Mark scheme
92Feb / March 2017 · Paper 12 · Q3Show mark scheme →
AH = T \cos 30
BT = H \sin 30
CW = T \sin 30
DW = T \cos 30
Mark scheme
93Feb / March 2017 · Paper 12 · Q13Show mark scheme →
A0.540 m
B0.960 m
C1.14 m
D1.36 m
Mark scheme
94Feb / March 2017 · Paper 12 · Q14Show mark scheme →
A4.0 | 6.0
B6.0 | 4.0
C6.0 | 8.0
D8.0 | 6.0
Mark scheme
95Oct / Nov 2016 · Paper 11 · Q15Show mark scheme →
A30 N, 50 N, 90 N with 50 cm and 30 cm distances
B36 N, 70 N, 106 N with 50 cm and 30 cm distances
C28 N, 35 N, 63 N with 50 cm and 30 cm distances
D42 N, 70 N, 112 N with 50 cm and 30 cm distances
Mark scheme
96Oct / Nov 2016 · Paper 11 · Q16Show mark scheme →
A[diagram A]
B[diagram B]
C[diagram C]
D[diagram D]
Mark scheme
97Oct / Nov 2016 · Paper 13 · Q15Show mark scheme →
A30 N and 50 N upwards, 90 N downwards; 50 cm and 30 cm spacing
B36 N and 70 N upwards, 106 N downwards; 50 cm and 30 cm spacing
C28 N and 35 N upwards, 63 N downwards; 50 cm and 30 cm spacing
D42 N and 70 N upwards, 112 N downwards; 50 cm and 30 cm spacing
Mark scheme
98Oct / Nov 2016 · Paper 13 · Q16Show mark scheme →
ADiagram A
BDiagram B
CDiagram C
DDiagram D
Mark scheme
99May / June 2016 · Paper 11 · Q12Show mark scheme →
ADiagram A
BDiagram B
CDiagram C
DDiagram D
Mark scheme
100May / June 2016 · Paper 11 · Q14Show mark scheme →
A3 kN
B15 kN
C30 kN
D60 kN
Mark scheme
101May / June 2016 · Paper 12 · Q12Show mark scheme →
Aarrow pointing up-right
Barrow pointing down-left
Carrow pointing left
Darrow pointing down-right
Mark scheme
102May / June 2016 · Paper 13 · Q12Show mark scheme →
Adiagram A
Bdiagram B
Cdiagram C
Ddiagram D
Mark scheme
103Feb / March 2016 · Paper 12 · Q2Show mark scheme →
A5.0 kN
B8.7 kN
C10 kN
D17 kN
Mark scheme
104Feb / March 2016 · Paper 12 · Q12Show mark scheme →
A25 N
B50 N
C75 N
D100 N
Mark scheme