Turning effects of forces — Paper 1 · A Level Physics 9702

13 A long uniform beam is pivoted at one end. A force of 300 N is applied to hold the beam horizontally. 0.5 m 2.5 m beam pivot 300 N What is the weight of the beam? A 300 N B 480 N C 600 N D 960 N

1 marks

Answer: B

This question in 9702/11 Oct/Nov 2004

12 A uniform beam of weight 100 N is pivoted at P as shown. Weights of 10 N and 20 N are attached to its ends. The length of the beam is marked off at 0.1 m intervals. At which point should a further weight of 20 N be attached to achieve equilibrium? 0.6 m 0.4 m 0.1 m A B C D P 10 N 20 N

1 marks

Answer: D

This question in 9702/11 Oct/Nov 2005

13 The diagram shows four forces applied to a circular object. 45 N 30 N 30 N 45 N Which of the following describes the resultant force and resultant torque on the object? resultant force resultant torque A non-zero non-zero B non-zero zero C zero non-zero D zero zero

1 marks

Answer: A

This question in 9702/11 Oct/Nov 2005

14 A force F is applied to a beam at a distance d from a pivot. The force acts at an angle θ to a line perpendicular to the beam. F θ pivot d Which combination will cause the largest turning effect about the pivot? F d θ A large large large B large large small C small small large D small large small

1 marks

Answer: B

This question in 9702/11 May/June 2006

15 A rigid uniform bar of length 2.4 m is pivoted horizontally at its mid-point. 0.8 m 0.8 m 200 N 300 N Weights are hung from two points of the bar as shown in the diagram. To maintain horizontal equilibrium, a couple is applied to the bar. What is the torque and direction of this couple? A 40 N m clockwise B 40 N m anticlockwise C 80 N m clockwise D 80 N m anticlockwise

1 marks

Answer: A

This question in 9702/11 May/June 2006

14 A rigid circular disc of radius r has its centre at X. A number of forces of equal magnitude F act at the edge of the disc. All the forces are in the plane of the disc. Which arrangement of forces provides a moment of magnitude 2Fr about X? A B F X X F F C D F X X F F F F

1 marks

Answer: B

This question in 9702/11 Oct/Nov 2006

13 Two 8.0 N forces act at each end of a beam of length 0.60 m. The forces are parallel and act in opposite directions. The angle between the forces and the beam is 60 °. 8.0 N 60° 0.60 m 60° 8.0 N What is the torque of the couple exerted on the beam? A 2.4 N m B 4.2 N m C 4.8 N m D 9.6 N m

1 marks

Answer: B

This question in 9702/11 May/June 2007

14 A uniform ladder rests against a vertical wall where there is negligible friction. The bottom of the ladder rests on rough ground where there is friction. The top of the ladder is at a height h above the ground and the foot of the ladder is at a distance 2a from the wall. The diagram shows the forces which act on the ladder. F ladder h W W F a a Which equation is formed by taking moments? A W a + F h = 2W a B F a + W a = F h C W a + 2W a = F h D W a – 2W a = 2F h

1 marks

Answer: A

This question in 9702/11 May/June 2008

14 Which pair of forces acts as a couple on the circular object? A B C D F F 2F F F 2F F F

1 marks

Answer: A

This question in 9702/11 Oct/Nov 2008

13 A spindle is attached at one end to the centre of a lever 1.20 m long and at its other end to the centre of a disc of radius 0.20 m. A cord is wrapped round the disc, passes over a pulley and is attached to a 900 N weight. 1.20 m F F spindle 0.20 m lever disc pulley cord 900 N What is the minimum force F, applied to each end of the lever, that could lift the weight? A 75 N B 150 N C 300 N D 950 N Space for working

1 marks

Answer: B

This question in 9702/11 May/June 2009

11 What is the centre of gravity of an object? A the geometrical centre of the object B the point about which the total torque is zero C the point at which the weight of the object may be considered to act D the point through which gravity acts

1 marks

Answer: C

This question in 9702/11 Oct/Nov 2009

13 The diagram shows two pulley wheels connected by a belt. P Q Wheel Q is driven by a motor and rotates clockwise at a constant rate. Wheel Q puts tension in the top portion of the belt, which in turn drives the wheel P. The lower portion of the belt is slack and has no tension. The weight of the belt and frictional forces are negligible. The diameter of P is 150 mm. The diameter of Q is 100 mm. The torque applied to Q is 3.0 N m. What is the tension in the belt and the torque on wheel P? tension in top of belt torque on wheel P / N / N m A 20 2.0 B 30 4.5 C 40 2.0 D 60 4.5

1 marks

Answer: D

This question in 9702/11 Oct/Nov 2009

10 What is the centre of gravity of an object? A the geometrical centre of the object B the point about which the total torque is zero C the point at which the weight of the object may be considered to act D the point through which gravity acts

1 marks

Answer: C

This question in 9702/12 Oct/Nov 2009

12 The diagram shows two pulley wheels connected by a belt. P Q Wheel Q is driven by a motor and rotates clockwise at a constant rate. Wheel Q puts tension in the top portion of the belt, which in turn drives the wheel P. The lower portion of the belt is slack and has no tension. The weight of the belt and frictional forces are negligible. The diameter of P is 150 mm. The diameter of Q is 100 mm. The torque applied to Q is 3.0 N m. What is the tension in the belt and the torque on wheel P? tension in top of belt torque on wheel P / N / N m A 20 2.0 B 30 4.5 C 40 2.0 D 60 4.5

1 marks

Answer: D

This question in 9702/12 Oct/Nov 2009

12 A spanner is used to tighten a nut as shown. 0.04 m 0.25 m F = 200 N A force F is applied at right-angles to the spanner at a distance of 0.25 m from the centre of the nut. When the nut is fully tightened, the applied force is 200 N. What is the resistive torque, in an anticlockwise direction, preventing further tightening? A 8 N m B 42 N m C 50 N m D 1250 N m Space for working

1 marks

Answer: C

This question in 9702/12 Oct/Nov 2010

14 A rigid L-shaped lever arm is pivoted at point P. P 5 N 2 m 2 m 10 N 3 m 1 m 15 N Three forces act on the lever arm, as shown in the diagram. What is the magnitude of the resultant moment of these forces about point P? A 15 N m B 20 N m C 35 N m D 75 N m

1 marks

Answer: A

This question in 9702/13 Oct/Nov 2010

15 Two parallel forces, each of magnitude F, act on a body as shown. F d s F What is the magnitude of the torque on the body produced by these forces? A F d B F s C 2F d D 2F s Space for working

1 marks

Answer: B

This question in 9702/13 Oct/Nov 2010

12 The diagram shows four forces applied to a circular object. 30 N 20 N 20 N 30 N Which row describes the resultant force and resultant torque on the object? resultant force resultant torque A zero zero B zero non-zero C non-zero zero D non-zero non-zero Space for working

1 marks

Answer: D

This question in 9702/11 May/June 2011

13 A uniform metre rule of mass 100 g is supported by a pivot at the 40 cm mark and a string at the 100 cm mark. The string passes round a frictionless pulley and carries a mass of 20 g as shown in the diagram. 0 20 40 60 80 100 20 g At which mark on the rule must a 50 g mass be suspended so that the rule balances? A 4 cm B 36 cm C 44 cm D 64 cm

1 marks

Answer: C

This question in 9702/11 May/June 2011

15 The diagrams all show a pair of equal forces acting on a metre rule. Which diagram shows forces that provide a couple and zero resultant force? A B C D

1 marks

Answer: B

This question in 9702/12 May/June 2011

11 The diagram shows four forces applied to a circular object. 30 N 20 N 20 N 30 N Which row describes the resultant force and resultant torque on the object? resultant force resultant torque A zero zero B zero non-zero C non-zero zero D non-zero non-zero Space for working

1 marks

Answer: D

This question in 9702/13 May/June 2011

12 A uniform metre rule of mass 100 g is supported by a pivot at the 40 cm mark and a string at the 100 cm mark. The string passes round a frictionless pulley and carries a mass of 20 g as shown in the diagram. 0 20 40 60 80 100 20 g At which mark on the rule must a 50 g mass be suspended so that the rule balances? A 4 cm B 36 cm C 44 cm D 64 cm Space for working

1 marks

Answer: C

This question in 9702/13 May/June 2011

14 A ruler of length 0.30 m is pivoted at its centre. Equal and opposite forces of magnitude 2.0 N are applied to the ends of the ruler, creating a couple as shown. 2.0 N 50° ruler pivot 50° 2.0 N What is the magnitude of the torque of the couple on the ruler when it is in the position shown? A 0.23 N m B 0.39 N m C 0.46 N m D 0.60 N m

1 marks

Answer: C

This question in 9702/11 Oct/Nov 2011

15 The diagram shows a child’s balancing game. 1 2 3 4 5 6 peg 7 8 9 10 11 12 13 14 15 one ring pivot two rings The wooden rod is uniform and all the rings are of equal mass. Two rings are hung on peg 13 and one on peg 1. On which hook must a fourth ring be hung in order to balance the rod? A 2 B 3 C 5 D 6 Space for working

1 marks

Answer: C

This question in 9702/11 Oct/Nov 2011

32 The diagram shows an insulating rod with equal and opposite point charges at each end. An electric field of strength E acts on the rod in a downwards direction. E +Q –Q Which row is correct? resultant force resultant torque A zero clockwise B downwards clockwise C zero anti-clockwise D downwards anti-clockwise

1 marks

Answer: C

This question in 9702/11 Oct/Nov 2011

13 Two co-planar forces act on the rim of a wheel. The forces are equal in magnitude. Which arrangement of forces provides only a couple? A B C D Space for working

1 marks

Answer: D

This question in 9702/12 Oct/Nov 2011

13 The diagram shows a child’s balancing game. 1 2 3 4 5 6 peg 7 8 9 10 11 12 13 14 15 one ring pivot two rings The wooden rod is uniform and all the rings are of equal mass. Two rings are hung on peg 13 and one on peg 1. On which hook must a fourth ring be hung in order to balance the rod? A 2 B 3 C 5 D 6 Space for working

1 marks

Answer: C

This question in 9702/13 Oct/Nov 2011

15 A ruler of length 0.30 m is pivoted at its centre. Equal and opposite forces of magnitude 2.0 N are applied to the ends of the ruler, creating a couple as shown. 2.0 N 50° ruler pivot 50° 2.0 N What is the magnitude of the torque of the couple on the ruler when it is in the position shown? A 0.23 N m B 0.39 N m C 0.46 N m D 0.60 N m

1 marks

Answer: C

This question in 9702/13 Oct/Nov 2011

31 The diagram shows an insulating rod with equal and opposite point charges at each end. An electric field of strength E acts on the rod in a downwards direction. E +Q –Q Which row is correct? resultant force resultant torque A zero clockwise B downwards clockwise C zero anti-clockwise D downwards anti-clockwise Space for working

1 marks

Answer: C

This question in 9702/13 Oct/Nov 2011

15 The diagram shows a solid cube with weight W and sides of length L. It is supported by a frictionless spindle that passes through the centres of two opposite vertical faces. One of these faces is shaded. L L to the right of its original position. The spindle is now removed and replaced at a distance 4 L 4 When viewing the shaded face, what is the torque of the couple that will now be needed to stop the cube from toppling? WL anticlockwise A 2 WL clockwise B 2 WL anticlockwise C 4 WL clockwise D 4 Space for working

1 marks

Answer: D

This question in 9702/12 May/June 2012

16 A student balances a 30 cm ruler on a fulcrum set at the 15 cm mark. She then places a 50 g mass on the 23 cm mark and a 20 g mass on the 11 cm mark, as shown. 20 g 50 g 0 7 11 23 30 Which mass should she place on the 7 cm mark to restore the balance? A 30 g B 40 g C 47 g D 133 g Space for working

1 marks

Answer: B

This question in 9702/11 Oct/Nov 2012

17 A rigid uniform beam is pivoted horizontally at its midpoint. Different vertical forces are applied to different positions on the beam. In which diagram is the beam in equilibrium? A B 10 N 5 cm 5 cm 4 cm 5 cm 10 N 10 N 15 N C D 2 cm 2 cm 5 cm 2.5 cm 2.5 cm 5 cm 5 N 5 N 10 N 15 N 14 N 15 N Space for working

1 marks

Answer: C

This question in 9702/12 Oct/Nov 2012

16 Four beams of the same length each have three forces acting on them. Which beam has both zero resultant force and zero resultant torque acting? A B 30 N 50 N 36 N 70 N 50 cm 30 cm 50 cm 30 cm 90 N 106 N C D 28 N 35 N 42 N 70 N 50 cm 30 cm 50 cm 30 cm 63 N 112 N Space for working

1 marks

Answer: D

This question in 9702/13 Oct/Nov 2012

14 A horizontal bar is supported on a pivot at its centre of gravity. A fixed load is attached to one end of the bar. To keep the bar in equilibrium, a force F is applied at a distance x from the pivot. x fixed load F How does F vary with x? A B C D F F F F 00 00 00 00 x x x x Space for working

1 marks

Answer: B

This question in 9702/11 May/June 2013

3 Two forces act on a circular disc as shown. 3 N 4 N Which diagram shows the line of action of the resultant force? A B C D 5 N 5 N 5 N 5 N Space for working

1 marks

Answer: A

This question in 9702/12 May/June 2013

14 A uniform beam of mass 1.4 kg is pivoted at P as shown. The beam has a length of 0.60 m and P is 0.20 m from one end. Loads of 3.0 kg and 6.0 kg are suspended 0.35 m and 0.15 m from the pivot as shown. 0.40 m 0.20 m 0.35 m 0.15 m 3.0 kg P 6.0 kg centre of beam of mass 1.4 kg What torque must be applied to the beam in order to maintain it in equilibrium? A 0.010 N m B 0.10 N m C 0.29 N m D 2.8 N m

1 marks

Answer: D

This question in 9702/12 May/June 2013

15 A uniform metre rule of weight 2.0 N is pivoted at the 60 cm mark. A 4.0 N weight is suspended from one end, causing the rule to rotate about the pivot. uniform metre rule 10 20 30 40 50 60 70 80 90 pivot weight 4.0 N At the instant when the rule is horizontal, what is the resultant turning moment about the pivot? A zero B 1.4 N m C 1.6 N m D 1.8 N m

1 marks

Answer: B

This question in 9702/11 Oct/Nov 2013

15 A uniform metre rule of weight 2.0 N is pivoted at the 60 cm mark. A 4.0 N weight is suspended from one end, causing the rule to rotate about the pivot. uniform metre rule 10 20 30 40 50 60 70 80 90 pivot weight 4.0 N At the instant when the rule is horizontal, what is the resultant turning moment about the pivot? A zero B 1.4 N m C 1.6 N m D 1.8 N m

1 marks

Answer: B

This question in 9702/12 Oct/Nov 2013

15 A diving board of length 5.0 m is hinged at one end and supported 2.0 m from this end by a spring of spring constant 10 kN m–1. A child of mass 40 kg stands at the far end of the board. mass of child 40 kg diving board 2.0 m spring hinge 5.0 m What is the extra compression of the spring caused by the child standing on the end of the board? A 1.0 cm B 1.6 cm C 9.8 cm D 16 cm Space for working

1 marks

Answer: C

This question in 9702/13 Oct/Nov 2013

12 A man holds a 100 N load stationary in his hand. The combined weight of the forearm and hand is 20 N. The forearm is held horizontal, as shown. F biceps forearm 4 cm 10 cm 20 N 32 cm 100 N What is the vertical force F needed in the biceps? A 750 N B 800 N C 850 N D 900 N Space for working

1 marks

Answer: C

This question in 9702/11 May/June 2014

13 A spindle is attached at one end to the centre of a lever of length 1.20 m and at its other end to the centre of a disc of radius 0.20 m. A string is wrapped round the disc, passes over a pulley and is attached to a 900 N weight. 1.20 m F F spindle 0.20 m lever disc pulley string 900 N What is the minimum force F, applied to each end of the lever, that could lift the weight? A 75 N B 150 N C 300 N D 950 N Space for working

1 marks

Answer: B

This question in 9702/11 May/June 2014

13 The diagram shows four forces applied to a circular object. 45 N 30 N 30 N 45 N Which of the following describes the resultant force and resultant torque on the object? resultant force resultant torque A non-zero non-zero B non-zero zero C zero non-zero D zero zero Space for working

1 marks

Answer: A

This question in 9702/12 May/June 2014

14 A uniform solid cuboid of concrete of dimensions 0.50 m × 1.20 m × 0.40 m and weight 4000 N rests on a flat surface with the 1.20 m edge vertical as shown in diagram 1. 0.40 m 0.40 m 1.20 m 0.50 m 0.50 m 1.20 m diagram 1 diagram 2 What is the minimum energy required to roll the cuboid through 90° to the position shown in diagram 2 with the 0.50 m edge vertical? A 200 J B 400 J C 1400 J D 2600 J Space for working

1 marks

Answer: A

This question in 9702/13 May/June 2014

15 A uniform beam is pivoted at P as shown. Weights of 10 N and 20 N are attached to its ends. The length of the beam is marked at 0.1 m intervals. The weight of the beam is 100 N. At which point should a further weight of 20 N be attached to achieve equilibrium? 0.6 m 0.4 m 0.1 m A B C D P 10 N 20 N

1 marks

Answer: D

This question in 9702/13 May/June 2014

12 A uniform ladder rests against a vertical wall where there is negligible friction. The bottom of the ladder rests on rough ground where there is friction. The top of the ladder is at a height h above the ground and the foot of the ladder is at a distance 2a from the wall. The diagram shows the forces that act on the ladder. F ladder h W W F a a Which equation is formed by taking moments? A W a + F h = 2W a B F a + W a = F h C W a + 2W a = F h D W a – 2W a = 2F h Space for working

1 marks

Answer: A

This question in 9702/11 Oct/Nov 2014

12 A uniform ladder rests against a vertical wall where there is negligible friction. The bottom of the ladder rests on rough ground where there is friction. The top of the ladder is at a height h above the ground and the foot of the ladder is at a distance 2a from the wall. The diagram shows the forces that act on the ladder. F ladder h W W F a a Which equation is formed by taking moments? A W a + F h = 2W a B F a + W a = F h C W a + 2W a = F h D W a – 2W a = 2F h Space for working

1 marks

Answer: A

This question in 9702/12 Oct/Nov 2014

14 A uniform metre rule of mass 100 g is supported by a pivot at the 40 cm mark and a string at the 100 cm mark. The string passes round a frictionless pulley and carries a mass of 20 g as shown in the diagram. 0 20 40 60 80 100 20 g At which mark on the rule must a 50 g mass be suspended so that the rule balances? A 4 cm B 36 cm C 44 cm D 64 cm

1 marks

Answer: C

This question in 9702/13 Oct/Nov 2014

15 A uniform metre rule is pivoted at the 34.0 cm mark, as shown. metre rule 4.0 cm 0 10 20 30 40 50 60 70 80 90 100 34.0 cm 64 g The rule balances when a 64 g mass is hung from the 4.0 cm mark. What is the mass of the metre rule? A 38 g B 44 g C 120 g D 136 g

1 marks

Answer: C

This question in 9702/11 May/June 2015

14 A ladder is positioned on icy (frictionless) ground and is leant against a rough wall. At the instant of release it begins to slide. Which diagram correctly shows the directions of the forces P, W and R acting on the ladder as it slides? A B P P ladder ladder wall wall R R W W ground ground C D P P ladder ladder wall wall R R W W ground ground

1 marks

Answer: B

This question in 9702/12 May/June 2015

15 Which pair of forces acts only as a couple on the circular object? A B C D F F 2F F F 2F F F

1 marks

Answer: A

This question in 9702/12 Oct/Nov 2015

14 Which statement best describes a couple? A a pair of forces of equal magnitude acting in opposite directions which produce rotational motion but not translational motion B a pair of forces of equal magnitude acting in opposite directions which produce translational motion but not rotational motion C a pair of forces of equal magnitude acting in the same direction which produce rotational motion but not translational motion D a pair of forces of equal magnitude acting in the same direction which produce translational motion but not rotational motion

1 marks

Answer: A

This question in 9702/13 Oct/Nov 2015

15 A cross-shaped structure, freely pivoted at O, has arms of lengths 5.0 m, 4.0 m, 3.0 m and 2.0 m. It is acted on by forces of 2.0 N, 3.0 N, 4.0 N and an unknown force F. The structure is in rotational equilibrium. F 5.0 m 2.0 N 2.0 m O 4.0 m 30° 3.0 N 3.0 m 4.0 N What is the magnitude of force F ? A 0.40 N B 2.0 N C 2.6 N D 4.4 N

1 marks

Answer: B

This question in 9702/13 Oct/Nov 2015

12 The diagram shows a uniform beam PQ. The length of the beam is 3.0 m and its weight is 50 N. The beam is supported on a pivot 1.0 m from end P. A load of weight W is hung from end P and the beam is in equilibrium. 3.0 m 1.0 m P Q W pivot What is the value of W ? A 25 N B 50 N C 75 N D 100 N

1 marks

Answer: A

This question in 9702/12 Feb/March 2016

13 Two forces, each of magnitude F, act at points V and W on an object. The two forces form a couple. The shape of the object is a right-angled triangle with sides of lengths x and y, as shown. F V y x W F Which expression gives the torque exerted by the couple? A Fx B Fy C 2Fx D 2Fy

1 marks

Answer: B

This question in 9702/12 Feb/March 2016

12 Forces are applied to a rigid body. The forces all act in the same plane. In which diagram is the body in equilibrium? A B C D F F F F 1 F 1 F 1 F 1 F 2 2 2 2 1 F 1 F 2 2 F F F F

1 marks

Answer: A

This question in 9702/11 May/June 2016

14 A trailer of weight 30 kN is attached to a cab at X, as shown in the diagram. cab trailer X 30 kN 10 m 10 m What is the upward force exerted at X by the cab on the trailer? A 3 kN B 15 kN C 30 kN D 60 kN

1 marks

Answer: B

This question in 9702/11 May/June 2016

14 Two coplanar forces act on the rim of a wheel. The forces are equal in magnitude. Which arrangement of forces provides only a couple? A B C D

1 marks

Answer: D

This question in 9702/12 May/June 2016

13 What is the centre of gravity of an object? A the geometrical centre of the object B the point at which the weight of the object may be considered to act C the point on the object about which there is a zero net torque D the point where gravity acts on the object

1 marks

Answer: B

This question in 9702/13 May/June 2016

14 A bicycle pedal is connected to a pivot by a metal bar, as shown. force 60 N pedal bar 12 cm 20 cm pivot 16 cm The force on the pedal is 60 N downwards. What is the moment of this force about the pivot? A 7.2 N m B 9.6 N m C 12 N m D 1200 N m

1 marks

Answer: B

This question in 9702/13 May/June 2016

15 Four beams of the same length each have three forces acting on them. Which beam has both zero resultant force and zero resultant torque acting? A B 30 N 50 N 36 N 70 N 50 cm 30 cm 50 cm 30 cm 90 N 106 N C D 28 N 35 N 42 N 70 N 50 cm 30 cm 50 cm 30 cm 63 N 112 N

1 marks

Answer: D

This question in 9702/11 Oct/Nov 2016

15 Four beams of the same length each have three forces acting on them. Which beam has both zero resultant force and zero resultant torque acting? A B 30 N 50 N 36 N 70 N 50 cm 30 cm 50 cm 30 cm 90 N 106 N C D 28 N 35 N 42 N 70 N 50 cm 30 cm 50 cm 30 cm 63 N 112 N

1 marks

Answer: D

This question in 9702/13 Oct/Nov 2016

12 A uniform metre rule of weight 2.0 N is pivoted at the 60 cm mark. A 4.0 N load is suspended from one end, causing the rule to rotate about the pivot. uniform metre rule 10 20 30 40 50 60 70 80 90 pivot load 4.0 N At the instant when the rule is horizontal, what is the resultant moment about the pivot? A 0.0 N m B 1.4 N m C 1.6 N m D 1.8 N m

1 marks

Answer: B

This question in 9702/12 Feb/March 2017

13 The vertical forces that the ground exerts on a stationary van are shown. 16 000 N 9000 N 0.600 m 1.500 m 0.400 m The van is 2.50 m long with the wheels at a distance of 0.600 m from the front of the van and 0.400 m from the rear of the van. What is the horizontal distance of the van’s centre of gravity from the front of the van? A 0.540 m B 0.960 m C 1.14 m D 1.36 m

1 marks

Answer: C

This question in 9702/12 Feb/March 2017

12 A sphere is acted upon by various forces, all of the same magnitude. Which system of forces provides a resultant torque but zero resultant force on the sphere? A B C D

1 marks

Answer: D

This question in 9702/11 May/June 2017

2 Two forces act on a circular disc as shown. 3 N 4 N Which diagram shows the line of action of the resultant force? A B C D 5 N 5 N 5 N 5 N

1 marks

Answer: A

This question in 9702/12 May/June 2017

11 In a machine, many couples act on a rotating object as shown. 25 N 50 N 30 N 16 N 6.5 cm 4.0 cm 16 N 30 N 10 cm 50 N 25 N 12 cm What is the resultant torque acting on the rotating object? A 4.7 N m B 8.6 N m C 9.3 N m D 17.1 N m

1 marks

Answer: C

This question in 9702/12 May/June 2017

11 A uniform beam of mass 1.4 kg is pivoted at P as shown. The beam has a length of 0.60 m and P is 0.20 m from one end. Loads of 3.0 kg and 6.0 kg are suspended 0.35 m and 0.15 m from the pivot as shown. 0.40 m 0.20 m 0.35 m 0.15 m 3.0 kg P 6.0 kg centre of beam of mass 1.4 kg What is the torque that must be applied to the beam in order to maintain it in equilibrium? A 0.010 N m B 0.10 N m C 0.29 N m D 2.8 N m

1 marks

Answer: D

This question in 9702/13 May/June 2017

13 A rigid circular disc of radius r has its centre at X. A number of forces of equal magnitude F act at the edge of the disc. All the forces are in the plane of the disc. Which arrangement of forces provides a moment of magnitude 2Fr about X? A B F X X F F C D F X X F F F F

1 marks

Answer: A

This question in 9702/11 Oct/Nov 2017

14 The diagram shows a motorised vehicle for carrying one person. direction of motion axle 400 mm 600 N 600 N The vehicle has two wheels on one axle. The passenger stands on a platform between the wheels. The weight of the machine is 600 N. Its centre of mass is 200 mm in front of the axle. The wheel radius is 400 mm. When stationary, a passenger of weight 600 N stands with his centre of mass 200 mm behind the axle to balance the machine. The motor is now switched on to provide a horizontal force of 90 N at the ground to move the vehicle forwards. How far and in which direction must the passenger move his centre of mass to maintain balance? A 60 mm backwards B 60 mm forwards C 140 mm backwards D 140 mm forwards

1 marks

Answer: B

This question in 9702/11 Oct/Nov 2017

12 The diagram shows a solid cube with weight W and sides of length L. It is supported at rest by a frictionless spindle that passes through the centres of two opposite vertical faces. One of these faces is shaded. L L to the right of its original position. The spindle is now removed and replaced at a distance 4 L 4 When viewing the shaded face, what is the torque of the couple that will now be needed to keep the cube at rest? WL anticlockwise A 4 WL clockwise B 4 WL anticlockwise C 2 WL clockwise D 2

1 marks

Answer: B

This question in 9702/12 Oct/Nov 2017

12 Two forces, each of magnitude F, act along the edges of a rectangular metal plate, as shown. a F b F P The plate has length a and width b. What is the torque about point P? A Fa B Fb C 2Fa D 2Fb

1 marks

Answer: B

This question in 9702/13 Oct/Nov 2017

11 The diagram shows four forces applied to a circular object. 45 N 30 N 30 N 45 N Which row describes the resultant force and resultant torque on the object? resultant force resultant torque A non-zero non-zero B non-zero zero C zero non-zero D zero zero

1 marks

Answer: A

This question in 9702/12 Feb/March 2018

10 A horizontal metal bar PQ of length 50.0 cm is hinged at end P. The diagram shows the metal bar viewed from above. 16.0 N 30° Q 5.0 N P 50.0 cm Two forces of 16.0 N and 5.0 N are in the horizontal plane and act on end Q as shown in the diagram. What is the total moment about P due to the two forces? A 1.5 N m B 4.4 N m C 6.5 N m D 9.4 N m

1 marks

Answer: A

This question in 9702/11 May/June 2018

12 Two parallel forces, each of magnitude F, act on a rod of length 5d. Which diagram shows the positions of the two forces that will produce the largest torque on the rod? A B F d F F F C D F 2d 2d F F F

1 marks

Answer: D

This question in 9702/11 May/June 2018

13 A uniform diving-board is held by two fixed rods at points P and Q. A person stands at end R of the diving-board, as shown. rod Q P rod R The forces exerted by the rods on the board are vertical. The board remains in equilibrium as the person slowly moves towards point Q from end R. Which row describes the changes to the forces exerted by the rods on the board? force at P force at Q A decreases decreases B decreases increases C increases decreases D increases increases

1 marks

Answer: A

This question in 9702/12 May/June 2018

14 Two forces, each of magnitude F, act in opposite directions on a rod. F P d d F Each force acts on the rod at a distance d from the pivot P. What is the torque of this couple about P? A 0 B F × d C 2F × d D 2F × 2d

1 marks

Answer: C

This question in 9702/12 May/June 2018

12 Which diagram shows a couple formed by two forces, each of magnitude F, acting on a rod? A B F F F F F C D F F F

1 marks

Answer: D

This question in 9702/13 May/June 2018

11 A uniform rod of length 200 cm is freely pivoted at point P. The rod is held horizontally in equilibrium by a 60 N weight that is attached to the rod by a string passing over a frictionless pulley. frictionless uniform rod pulley 40 cm 30° P 200 cm weight 60 N What is the weight of the rod? A 30 N B 60 N C 80 N D 140 N

1 marks

Answer: C

This question in 9702/11 Oct/Nov 2018

12 A uniform rectangular board is supported by a frictionless pivot at its centre point P. R 2.5F 20 cm P Q F Two forces act in the plane of the board. Force F acts at corner Q and force 2.5F acts at corner R. The perpendicular distance between the line of action of force F and point P is 20 cm. The board is in equilibrium. What is the area of the board? A 160 cm2 B 320 cm2 C 640 cm2 D 1600 cm2

1 marks

Answer: C

This question in 9702/12 Oct/Nov 2018

12 A flat metal disc has radius R. Forces of magnitude F are applied tangentially at the edge of the disc. The forces are in the plane of the disc. Which arrangement of forces produces only a torque of magnitude 2FR ? A B C D F F 2F 2F R R R R F 2F F 2F

1 marks

Answer: B

This question in 9702/13 Oct/Nov 2018

12 A fairground ride consists of four carriages connected to a central vertical pole, as shown in the following view from above. direction vertical of rotation central pole not to scale carriages A motor rotates the central pole about its axis. This results in the four carriages each moving along a circular path. The distance from the middle of each carriage to the centre of the pole is 3.20 m. When they are moving, each carriage experiences an air resistance force of 85.0 N. Assume that there are no other significant resistive forces. Which torque does the motor need to apply to the pole to keep the system rotating at constant maximum speed? A 5.44 N m B 272 N m C 544 N m D 1090 N m

1 marks

Answer: D

This question in 9702/12 Feb/March 2019

13 A uniform horizontal beam OX, 4.0 m long and weighing 100 N, is hinged at a wall at point O. It is supported by a cord XY which is attached to the wall at Y. Y cord O 30° X 4.0 m What is the tension in the cord? A 50 N B 58 N C 86 N D 100 N

1 marks

Answer: D

This question in 9702/12 Feb/March 2019

13 A couple is applied to a tap as shown. F pivot tap d d F What is the torque of the couple? Fd A B Fd C 2Fd D 4Fd 2

1 marks

Answer: C

This question in 9702/11 May/June 2019

12 A shop sign weighing 75 N hangs from a frame attached to a vertical wall. Z 30° X Y 0.50 m wall sign weight 75 N The frame consists of a horizontal rod XY and a rod YZ that is at an angle of 30° to the horizontal. Rod XY is attached to the wall by a hinge at X and has length 0.50 m. Assume that the weights of the rods are negligible. What is the horizontal force exerted by the wall on rod XY? A 0 N B 43 N C 130 N D 150 N

1 marks

Answer: C

This question in 9702/13 May/June 2019

13 What is the torque of the couple shown? 15 N 15.0 cm 5.0 cm 15 N A 0.75 N m B 1.50 N m C 3.00 N m D 5.25 N m

1 marks

Answer: A

This question in 9702/13 May/June 2019

12 Which diagram shows a couple? F A F B F F C F D F F

1 marks

Answer: A

This question in 9702/11 Oct/Nov 2019

11 A rigid uniform bar of length 2.4 m is pivoted horizontally at its midpoint. 0.8 m 0.8 m 200 N 300 N Weights are hung from two points on the bar as shown in the diagram. To maintain equilibrium, a couple is applied to the bar. What is the torque and direction of this couple? A 40 N m clockwise B 40 N m anticlockwise C 80 N m clockwise D 80 N m anticlockwise

1 marks

Answer: A

This question in 9702/12 Oct/Nov 2019

11 The diagram shows two pairs X and Y of parallel forces. X Y 20 N 40 N 50 cm 50 cm 40 N 20 N Which statement is correct? A X is equivalent to a clockwise torque of 10 N m and a force of 20 N to the left. B X is equivalent to a clockwise torque of 20 N m only. C Y is equivalent to an anticlockwise torque of 30 N m and a force of 20 N to the left. D Y is equivalent to an anticlockwise torque of 30 N m only.

1 marks

Answer: A

This question in 9702/13 Oct/Nov 2019

12 A uniform rod of weight 20 N and length 2.0 m is acted upon by two vertical forces, as shown. 15 N 5.0 N What are the resultant force acting on the rod and the resultant moment about the centre of gravity of the rod? resultant force resultant moment / N / N m A 0 10 B 0 20 C 20 10 D 20 20

1 marks

Answer: A

This question in 9702/12 Feb/March 2020

12 Which statement best describes a couple? A a pair of forces of equal magnitude acting in opposite directions which produce rotational motion but not translational motion B a pair of forces of equal magnitude acting in opposite directions which produce translational motion but not rotational motion C a pair of forces of equal magnitude acting in the same direction which produce rotational motion but not translational motion D a pair of forces of equal magnitude acting in the same direction which produce translational motion but not rotational motion

1 marks

Answer: A

This question in 9702/11 May/June 2020

13 A uniform rod XY of weight 10.0 N is freely hinged to a wall at X. It is held horizontal by a force F acting from Y at an angle of 30° to the horizontal, as shown. F wall 60° 30° X Y 10.0 N What is the value of F ? A 5.0 N B 8.7 N C 10.0 N D 20.0 N

1 marks

Answer: C

This question in 9702/11 May/June 2020

11 A bicycle pedal is connected to a pivot by a metal bar, as shown. force 60 N pedal bar 12 cm 20 cm pivot 16 cm The force on the pedal is 60 N downwards. What is the moment of this force about the pivot? A 7.2 N m B 9.6 N m C 12 N m D 1200 N m

1 marks

Answer: B

This question in 9702/12 May/June 2020

12 Two forces, each of magnitude F, act along the edges of a rectangular metal plate, as shown. a F b F P The plate has length a and width b. What is the torque about point P? A Fa B Fb C 2Fa D 2Fb

1 marks

Answer: B

This question in 9702/13 May/June 2020

13 A non-uniform rod has a mass of 100 g and a length of 50 cm. It is supported by a chain at its midpoint. The rod is held in equilibrium by having a mass of 60 g suspended from its right-hand end, as shown. centre non-uniform rod of gravity chain supporting the of mass 100 g of rod rod at its midpoint 50 cm d mass 60 g The centre of gravity of the rod is a distance d from its left-hand end. What is the value of d ? A 10 cm B 15 cm C 25 cm D 40 cm

1 marks

Answer: A

This question in 9702/13 May/June 2020

12 Two people push a vertical gate to open it. The forces exerted by the people on the gate are shown. One person is distance d, from the gate’s hinge and pushes with horizontal force F, at angle 4 to the gate. The other person is at distance d2 from the hinge and pushes with horizontal force F2 at an angle @, to the gate. What is the total moment about the hinge due to forces F, and F2? A (d,x F,cos 6) + (d2 x F.cos @) B (d,xF,sin@) + (d2x Fosin&) C (d; x Fxcos @,) — (d2 x Focos &) D (d,xF,sin@) — (d2 x Fosin &)

1 marks

Answer: B

This question in 9702/11 Oct/Nov 2020

12 A rigid circular disc of radius r has its centre at X. A number of forces of equal magnitude F act at the edge of the disc. All the forces are in the plane of the disc. Which arrangement of forces provides a total moment of magnitude 2Fr about X? A B F X X F F C D F X X F F F F

1 marks

Answer: A

This question in 9702/12 Oct/Nov 2020

12 A couple applies a clockwise torque of 9.0 N m to a circular disc. Which diagram shows this couple? A B 9.0 N 45 N 50 cm 20 cm 9.0 N 45 N C D 45 N 9.0 N 10 cm 100 cm 45 N 9.0 N

1 marks

Answer: B

This question in 9702/13 Oct/Nov 2020

12 Two parallel forces, each of magnitude F, act on a rod of length 5d. Which diagram shows the positions of the two forces that will produce the largest torque on the rod? A B F d F F F C D F 2d 2d F F F

1 marks

Answer: D

This question in 9702/12 Feb/March 2021

12 Which pair of forces forms a couple with a torque of 30 N m? A B 30 N 40 N 1.0 m 2.0 m 10 N 30 N C D 25 N 15 N 1.0 m 2.0 m 5 N 15 N

1 marks

Answer: D

This question in 9702/11 May/June 2021

13 A uniform rigid bar XZ with negligible mass is 1.20m long. The bar is pivoted at point P. Three coplanar forces act on the bar as shown. Forces of 16N and 20N act perpendicularly to the bar at points X and Y respectively. Force F acts at point Z at an angle of 30° to the axis of the bar. The distances along the bar of the pivot and of the forces are shown. The bar experiences a resultant moment about P of 6.0Nm in a clockwise direction. What is the magnitude of F? A 9.2N B 11N C 16N D 24N

1 marks

Answer: C

This question in 9702/11 May/June 2021

12 What is a couple? A a pair of equal forces acting in the same direction but along different lines B a pair of forces that are equal and opposite but acting along different lines C a pair of forces that produce no resultant force and no resultant moment D a pair of unequal forces acting in opposite directions but along the same line

1 marks

Answer: B

This question in 9702/13 May/June 2021

13 Four coplanar forces act on a rigid rod, as shown. The rod is hinged at P. Which force produces the greatest moment about point P? 6 N 2 N B 4 N D P 30° C 30° 1.0 m 1.0 m 1.0 m 1.0 m A 10 N

1 marks

Answer: A

This question in 9702/13 May/June 2021

14 A book of weight W has a rectangular shape and is of uniform thickness. The book is held in a vertical plane so that the longer sides of the book are vertical, as shown. hand b book a Which expression gives the approximate torque exerted by the hand on the book? A Wa clockwise 2 B Wb anticlockwise 2 C Wa clockwise D Wb anticlockwise

1 marks

Answer: A

This question in 9702/13 May/June 2021

12 Ashelf XY is 0.40 m long and is attached to a wall at end X. It is kept horizontal by a wire attached to Y and to the wall, as shown. 0.40m The tension force in the wire is 15N at an angle of 30° to the horizontal. What is the moment of this force about point X? A 3.0Nm B 5.2Nm C 69Nm D 12Nm

1 marks

Answer: A

This question in 9702/11 Oct/Nov 2021

13 A statement about the principle of moments with some words omitted is shown. ‘For an object in a state of rotational equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about … .’ Which words correctly complete the statement? A any point B the centre of gravity of the object C the pivot D the same point

1 marks

Answer: D

This question in 9702/11 Oct/Nov 2021

12 Two forces act as a couple. Which statement about the two forces must not be correct? A They act along the same straight line. B They act in opposite directions. C They are the same type of force. D They have the same magnitude.

1 marks

Answer: A

This question in 9702/13 Oct/Nov 2021

13 A sign outside a shop is suspended from a rusty horizontal hinge at its top end. The sign hangs in equilibrium at an angle of 25° to the vertical, as shown. The sign is a square of side length 52cm and uniform thickness. It has a mass of 36 kg. What is the moment of the weight of the sign about the hinge? A 39Nm B 78Nm C 83Nm D 92Nm

1 marks

Answer: A

This question in 9702/13 Oct/Nov 2021

14 A uniform rod of length 200 cm is freely pivoted at point P. The rod is held horizontally in equilibrium by a 60 N weight that is attached to the rod by a string passing over a frictionless pulley. string frictionless uniform rod pulley 40 cm 30° P 200 cm weight 60 N What is the weight of the rod? A 30 N B 60 N C 80 N D 140 N

1 marks

Answer: C

This question in 9702/13 Oct/Nov 2021

11 A horizontal metal bar PQ of length 50.0 cm is hinged at end P. The diagram shows the metal bar viewed from above. 16.0 N 30° Q 5.0 N P 50.0 cm Two forces of 16.0 N and 5.0 N are in the horizontal plane and act on end Q, as shown. What is the resultant moment about P due to the two forces? A 1.5 N m B 4.4 N m C 6.5 N m D 9.4 N m

1 marks

Answer: A

This question in 9702/12 Feb/March 2022

11 A horizontal wooden plank is pivoted at one end, as shown. centre of gravity plank pivot 4 m 10 m The plank has a mass of 100 kg and a length of 10 m. The centre of gravity of the plank is a distance of 4 m from the pivot. What is the moment of the weight of the plank about the pivot? A 4  102 N m B 5  102 N m C 4  103 N m D 5  103 N m

1 marks

Answer: C

This question in 9702/11 May/June 2022

11 Two forces form a couple. Which statement describes the two forces? A They are in the same direction. B They are perpendicular to each other. C They have the same magnitude. D They pass through the same point.

1 marks

Answer: C

This question in 9702/12 May/June 2022

13 A diving board of length 5.0 m is hinged at one end and supported 2.0 m from this end by a spring of spring constant 10 kN m–1. A child of mass 40 kg stands at the far end of the board. mass of child 40 kg diving board 2.0 m spring hinge 5.0 m What is the extra compression of the spring caused by the child standing on the end of the board? A 1.0 cm B 1.6 cm C 9.8 cm D 16 cm

1 marks

Answer: C

This question in 9702/12 May/June 2022

11 A square board, of side length x, hangs freely from a nail P, as shown. The board has uniform thickness and is made from material of uniform density. P Q x 2x x 2x A second square board, of side length 2x, is made of the same material and has the same thickness as the original board. This second board is then hung from a nail Q. Nails P and Q are at the same height. What is the vertical distance between the positions of the centres of gravity of the two boards? x A 0 B C x D x 2 2

1 marks

Answer: B

This question in 9702/11 Oct/Nov 2022

13 A rigid rod XY has negligible mass and length 75 cm. The rod is suspended from a fixed point P by a string attached to end X. An object of mass 11 kg is suspended by a string that is attached to the rod at a distance of 25 cm from end X, as shown. P 75 cm X Y 25 cm 11 kg Which vertically upward force acting on end Y of the rod would hold the rod horizontally in equilibrium? A 3.7 N B 33 N C 36 N D 320 N

1 marks

Answer: C

This question in 9702/11 Oct/Nov 2022

12 What is not a necessary requirement of the forces in a couple? A They act in opposite directions. B They act along different lines. C They have the same magnitude. D They produce a resultant force.

1 marks

Answer: D

This question in 9702/12 Oct/Nov 2022

13 A box of length 12 cm and weight 0.43 N is placed on a horizontal table, with the greater part of its length overhanging the edge of the table. The edge of the table acts as a pivot. The centre of gravity of the box is at its geometric centre. To balance the box, a uniform sphere of diameter 2.4 cm is placed inside the box, touching one end, as shown. 12 cm box 2.4 cm sphere table edge of table (pivot) Assume that the forces acting on the box are in the plane of the diagram. What is the minimum mass of the sphere that is needed to maintain the system in equilibrium? A 0.066 kg B 0.13 kg C 0.22 kg D 1.3 kg

1 marks

Answer: B

This question in 9702/12 Oct/Nov 2022

11 Which diagram shows a couple formed by two forces, each of magnitude F, acting on a rod? A B F F F F C F D F F F

1 marks

Answer: D

This question in 9702/13 Oct/Nov 2022

12 A student states that: ‘If an object is in equilibrium, the sum of the clockwise moments about a point X is equal to the sum of the anticlockwise moments about a point Y.’ Which condition would make the student’s statement correct? A Either X or Y is the centre of gravity of the object. B Either X or Y is the pivot of the object. C X and Y are at opposite ends of the object. D X and Y are the same point on the object.

1 marks

Answer: D

This question in 9702/13 Oct/Nov 2022

13 Auniform rod of length 30cm and weight 5.2 N is attached to a wall by a hinge at one end. The other end of the rod is supported by a wire so that the rod is horizontal and in equilibrium. The wire is at an angle of 40° to the horizontal. wall hinge What is the tension in the wire? A 3.4N B 4.0N C 6.8N D 8.1N

1 marks

Answer: B

This question in 9702/13 Oct/Nov 2022

11 A satellite uses two thrusters to adjust its motion in space. Each thruster exerts a force of 40 N on the satellite. The line of action of each force is a perpendicular distance of 2.3 m from the centre of gravity of the satellite. These two parallel forces act in opposite directions. 40 N 2.3 m thruster thruster 2.3 m 40 N satellite What are the magnitudes of the torque and the resultant force acting on the satellite due to the two thrust forces? torque resultant / N m force / N A 92 0 B 92 80 C 180 0 D 180 80

1 marks

Answer: C

This question in 9702/12 Feb/March 2023

15 What is the centre of gravity of an object? A the geometrical centre of the object B the point at which the weight of the object may be considered to act C the point on the object about which there is a zero net torque D the point where gravity acts on the object

1 marks

Answer: B

This question in 9702/12 Feb/March 2023

11 The driver of a car applies two parallel forces to a steering wheel, as shown. centre of steering wheel 15 N 65° 65° 15 N 0.40 m Each force has a magnitude of 15 N and acts in the direction shown. The steering wheel has a diameter of 0.40 m. What is the torque exerted on the steering wheel? A 1.3 N m B 2.5 N m C 2.7 N m D 5.4 N m

1 marks

Answer: D

This question in 9702/11 May/June 2023

12 A farmer is trying to lift the corner of a large water tank. She uses a metal rod as a lever. force from farmer metal rod water tank pivot The vertical force from the farmer is constant and is always applied to the end of the rod. Which change must increase the upward force on the water tank? A using a longer rod and moving the pivot closer to the tank B using a longer rod and moving the pivot further away from the tank C using a shorter rod and moving the pivot closer to the tank D using a shorter rod and moving the pivot further away from the tank

1 marks

Answer: A

This question in 9702/11 May/June 2023

11 A rod is pivoted at point O. A force F is applied to the rod at point W, as shown. F X rod W O Y What is the moment of the force F about O? A F  distance OX B F  distance OY C F  distance WO D F  distance WX

1 marks

Answer: B

This question in 9702/12 May/June 2023

11 What is not a requirement for two forces to act as a couple? A The two forces act in opposite directions. B The two forces act through the same point. C The two forces combine to produce zero resultant force. D The two forces have equal magnitude.

1 marks

Answer: B

This question in 9702/13 May/June 2023

12 A uniform metre rule is pivoted at the 34.0 cm mark, as shown. metre rule 4.0 cm 0 10 20 30 40 50 60 70 80 90 100 34.0 cm 64 g The rule balances when a 64 g mass is hung from the 4.0 cm mark. What is the mass of the metre rule? A 38 g B 44 g C 120 g D 136 g

1 marks

Answer: C

This question in 9702/13 May/June 2023

11 A force F is applied at an angle of 45° to a door handle at a distance d from the pivot of the handle, as shown. ° i t 48 handle pIvo What is the moment of the force about the pivot? Fd B Fd Cc FaV2 D 2Fd J2

1 marks

Answer: A

This question in 9702/12 Oct/Nov 2023

12 A couple consists of two forces, each of magnitude F, that act in opposite directions in the same plane. The perpendicular distance between the two forces is d. F d F What is the torque of the couple? Fd F A B C Fd D 2Fd 2 d

1 marks

Answer: C

This question in 9702/12 Oct/Nov 2023

11 A uniform rigid beam of length 3.2m is pivoted at its centre. Two children sit at the opposite ends of the beam, as shown. child mass 24 kg child mass 36 kg One child has a mass of 24 kg. The other child has a mass of 36 kg. The heavier child causes one end of the beam to permanently rest on the ground, so that the beam makes an angle of 20° to the horizontal ground. What is the moment of the weight of the 24 kg child about the pivot? A 72Nm B 130Nm C 350Nm D 380Nm

1 marks

Answer: C

This question in 9702/13 Oct/Nov 2023

13 Arod is pivoted at one end. Initially the angle @ of the rod to the horizontal is 0°. The weight of the rod causes a moment M about the pivot. The rod is then rotated in the vertical plane so that the angle @ of the rod increases from 0° to 180°. Which graph shows the variation of M with 0? A B M M 0 0 0 90° 180° 0 90° 180° 0 0 oO D M M 0 0 90° 180° 0 90 180° 0 0

1 marks

Answer: D

This question in 9702/12 Feb/March 2024

15 A uniform beam PQ rests horizontally on a support at point S. 2.5m rope support A rope is attached at one end of the beam. The rope is at an angle of 60° to the vertical and exerts a force F, in newtons, on the beam. What is the moment, in Nm, of the force F about the point S? A 1.1F B 1.3F C 1.9F D 2.2F

1 marks

Answer: A

This question in 9702/11 May/June 2024

11 Two forces act on an object. Which diagram represents a couple? A B C D 6 N 6 N 6 N 6 N 6 N 6 N 12 N 12 N

1 marks

Answer: B

This question in 9702/12 May/June 2024

10 The diagram shows the view from above of a sprinkler system used to water a garden. direction of pivot of water jet sprinkler tube 0.15 m The sprinkler consists of a tube of length 0.15 m. The tube is pivoted in the middle and spins in a horizontal plane as it lets out jets of water from each end. The two water jets are in opposite directions to each other. Each water jet exerts a horizontal force of 3.0 N on the tube at right angles to the tube. What is the magnitude of the torque on the tube from the water jets? A 0 N m B 0.23 N m C 0.45 N m D 0.90 N m

1 marks

Answer: C

This question in 9702/13 May/June 2024

16 A uniform bar of weight 200N and length 4.0m is freely hinged on a wall at one end. The bar is horizontal and is held in equilibrium by a cable attached at a distance of 0.50m from the other end. The cable is at an angle of 35° to the horizontal. wall '(0.50m _—$ @ i —_—\—o@°$ >——_— What is the tension T in the cable? A 140N B 170N C 200N D 400N

1 marks

Answer: C

This question in 9702/11 Oct/Nov 2024

17 The diagrams all show a pair of equal forces acting on a metre rule. Which diagram shows forces that provide a couple and zero resultant force? A B C D

1 marks

Answer: B

This question in 9702/11 Oct/Nov 2024

13 Four forces act about a point P, as shown. S.ON x 5.0N The forces act in the same plane and produce no resultant moment about point P. What is the length XY? A 6.9m B 12m C 14m D 24m

1 marks

Answer: C

This question in 9702/12 Oct/Nov 2024

13 Which statement correctly describes a couple? A A couple is a pair of forces that act in the same direction. B A couple is a pair of forces that act on the centre of gravity of an object. C A couple is a pair of forces that act to produce a resultant force. D A couple is a pair of forces that act to produce rotation only.

1 marks

Answer: D

This question in 9702/13 Oct/Nov 2024

14 A uniform beam of mass 1.4 kg is pivoted at P, as shown. The beam has a length of 0.60 m and P is a distance of 0.20 m from one end. Loads of 3.0 kg and 6.0 kg are suspended at distances of 0.35 m and 0.15 m from the pivot, as shown. 0.40 m 0.20 m 0.35 m 0.15 m 3.0 kg P 6.0 kg centre of beam of mass 1.4 kg What is the torque that must be applied to the beam in order to maintain it in equilibrium? A 0.010 N m B 0.10 N m C 0.29 N m D 2.8 N m

1 marks

Answer: D

This question in 9702/13 Oct/Nov 2024

9 The diagram shows a child X of mass 20 kg and a child Y of mass 15 kg seated on a uniform plank. child X child Y mass 20 kg mass 15 kg pivot plank mass 7.0 kg The plank has a mass of 7.0 kg and has a pivot at its midpoint. The plank is horizontal and in equilibrium. Which statement about the weight of the plank is correct? A The weight of the plank can be considered to be acting at its midpoint. B The weight of the plank is causing an anticlockwise moment. C The weight of the plank is causing a clockwise moment. D The weight of the plank equals the force on the plank from the pivot.

1 marks

Answer: A

This question in 9702/12 Feb/March 2025

11 A shop sign weighing 75 N hangs from a frame attached to a vertical wall. Z 30° X Y 0.50 m wall sign weight 75 N The frame consists of a horizontal rod XY and a rod YZ that is at an angle of 30° to the horizontal. Rod XY is attached to the wall by a hinge at X and has length 0.50 m. Assume that the weights of the rods are negligible. What is the horizontal force exerted by the wall on rod XY? A 0 N B 43 N C 130 N D 150 N

1 marks

Answer: C

This question in 9702/12 Feb/March 2025

13 The diagram shows a uniform plank XY of length 4.0 m and weight 300 N. child plank X Y support 4.0 m The plank rests on fixed supports at its ends X and Y. A child of weight 600 N stands in different positions on the plank. The support at end X exerts a force F vertically upwards on the plank. What is the magnitude of F when the child stands at X and when the child stands at Y? F / N when F / N when child is at X child is at Y A 600 0 B 600 150 C 750 0 D 750 150

1 marks

Answer: D

This question in 9702/12 Feb/March 2025

13 Which row describes a pair of forces that forms a couple? direction of magnitude of the forces the forces A opposite different B opposite equal C same different D same equal

1 marks

Answer: B

This question in 9702/11 May/June 2025

15 A student balances a 30 cm ruler on a fulcrum set at the 15 cm mark. She then places a 50 g mass on the 23 cm mark and a 20 g mass on the 11 cm mark, as shown. 20 g 50 g 0 7 11 23 30 Which mass should she place on the 7 cm mark to restore the balance? A 30 g B 40 g C 47 g D 133 g

1 marks

Answer: B

This question in 9702/11 May/June 2025

15 A square shop sign of uniform density has mass 2.4 kg and sides of length 0.86 m. The sign is supported by a hinge along its top edge. There is friction in the hinge so that the sign hangs from it in equilibrium at an angle of 15° to the vertical, as shown. hinge 0.86 m sign 15° What is the moment about the hinge of the weight of the sign? A 2.6 N m B 4.0 N m C 5.2 N m D 9.8 N m

1 marks

Answer: A

This question in 9702/12 May/June 2025

17 The diagram shows a couple. force perpendicular distance between the forces force How is the torque of the couple calculated? 1  perpendicular distance between the forces  magnitude of one of the forces A 2 B perpendicular distance between the forces  magnitude of one of the forces C perpendicular distance between the forces  magnitude of the sum of the forces D 2  perpendicular distance between the forces  magnitude of one of the forces

1 marks

Answer: B

This question in 9702/12 May/June 2025

12 A non-uniform bar PQ has length 50 cm and weight 200 N. 360 N non-uniform bar block P Q 50 cm A block of weight 400 N is attached to the top of the bar at its centre. The bar rests on horizontal ground. A vertical force of 360 N is now exerted upwards on the bar at end Q and is just sufficient to lift end Q from the ground. What is the distance from the centre of gravity of the bar to end P? A 0.050 m B 0.10 m C 0.25 m D 0.40 m

1 marks

Answer: D

This question in 9702/13 May/June 2025

10 Which statement about a couple is correct? A It acts to produce both translational motion and rotation. B It acts to produce rotation only. C It acts to produce translational motion only. D It acts to produce neither rotation nor translational motion.

1 marks

Answer: B

This question in 9702/14 May/June 2025

13 A uniform rod of weight 28 N is supported at one end by force F. The rod is in equilibrium and attached to a frictionless hinge at end X. F rod 40° X 28 N What is the magnitude of F ? A 9.0 N B 11 N C 18 N D 21 N

1 marks

Answer: B

This question in 9702/11 Oct/Nov 2025

14 Two forces, each of magnitude F, act in opposite directions on a rod. F P d d F Each force acts on the rod at a distance d from the pivot P. What is the torque of this couple about P? A 0 B F  d C 2F  d D 2F  2d

1 marks

Answer: C

This question in 9702/11 Oct/Nov 2025

13 Which diagram shows a couple? A B F F F F C D F F F

1 marks

Answer: A

This question in 9702/12 Oct/Nov 2025

14 The diagram shows a uniform bar of mass M and length L resting on a pivot at a distance x from end X. L x X An object of mass m is placed on the bar at distance y from the pivot so that the bar is in equilibrium. What is an expression for y? xM M (L – x) M 1 (Lm – xM ) A B C (L – 2x) D m m 2 m m

1 marks

Answer: C

This question in 9702/12 Oct/Nov 2025

13 A uniform rod of weight 28 N is supported at one end by force F. The rod is in equilibrium and attached to a frictionless hinge at end X. F rod 40° X 28 N What is the magnitude of F ? A 9.0 N B 11 N C 18 N D 21 N

1 marks

Answer: B

This question in 9702/13 Oct/Nov 2025

14 Two forces, each of magnitude F, act in opposite directions on a rod. F P d d F Each force acts on the rod at a distance d from the pivot P. What is the torque of this couple about P? A 0 B F  d C 2F  d D 2F  2d

1 marks

Answer: C

This question in 9702/13 Oct/Nov 2025

13 A uniform rod is attached by a hinge at one end to a wall. The other end of the rod is supported by a wire so that the rod is horizontal and in equilibrium. wire wall hinge rod Which arrow shows the direction of the force on the rod from the hinge? A B C D

1 marks

Answer: D

This question in 9702/14 Oct/Nov 2025

14 A couple is applied to a tap, as shown. F pivot tap d d F What is the torque of the couple? Fd A B Fd C 2Fd D 4Fd 2

1 marks

Answer: C

This question in 9702/14 Oct/Nov 2025

15 A uniform beam rests on two supports, X and Y, as shown. X Y 700 N 200 N 6.0 m 10.0 m 20.0 m not to scale The beam has length 20.0 m and weight 200 N. A man of weight 700 N stands on the beam at a distance of 6.0 m from support X. The beam is in equilibrium. What is the contact force of support X on the beam? A 310 N B 450 N C 590 N D 900 N

1 marks

Answer: C

This question in 9702/14 Oct/Nov 2025