Equilibrium of concurrent forces - Question Bank

1. Which of the following statements is NOT true for a system of concurrent forces in equilibrium?
A) The vector sum of the forces is zero.
B) The resultant force is zero.
C) The net acceleration of the particle is zero.
D) The net torque about any point is zero.
2. Consider a particle in equilibrium under the action of three forces. If the angle between two forces is 90 degrees, and the angle between the first force and the third force is 150 degrees, what is the angle between the second and third force?
A) 120 degrees
B) 150 degrees
C) 90 degrees
D) 60 degrees
3. If a particle is in equilibrium, and we apply a force F to it, the particle will start to move if F is:
A) Zero
B) Non-zero
C) Equal to the sum of other forces
D) Opposite to the sum of other forces
4. A system of concurrent forces is in equilibrium. If we consider a closed polygon formed by representing these forces as vectors head-to-tail, what can be said about the polygon?
A) It is an open polygon.
B) It is a closed polygon.
C) It is a straight line.
D) It collapses to a point.
5. Three concurrent forces of magnitudes F1, F2, and F3 are in equilibrium. If F1 = 5 N and F2 = 12 N, what is the possible magnitude of F3?
A) 7 N
B) 17 N
C) 13 N
D) Any value between 7 N and 17 N
6. If a particle is in equilibrium, the rate of change of its linear momentum is:
A) Maximum
B) Minimum
C) Zero
D) Constant
7. Lami's Theorem is a consequence of which fundamental law of motion?
A) Newton's First Law
B) Newton's Second Law
C) Newton's Third Law
D) Law of Conservation of Energy
8. A system of concurrent forces is in equilibrium. If we add a new force that is equal in magnitude and opposite in direction to the resultant of the original forces, the system will then be:
A) In equilibrium.
B) Not in equilibrium.
C) Rotating.
D) Accelerating.
9. If a particle is in equilibrium under the action of two forces, F1 and F2, what is the relationship between their magnitudes and directions?
A) Equal magnitudes, same direction.
B) Equal magnitudes, opposite directions.
C) Different magnitudes, opposite directions.
D) Different magnitudes, same direction.
10. Consider a scenario where a ladder is leaning against a wall. The forces acting on the ladder are weight, normal force from the ground, friction from the ground, and normal force from the wall. For the ladder to be in equilibrium, what conditions must be met?
A) Sum of vertical forces = 0, sum of horizontal forces = 0.
B) Sum of vertical forces = 0, sum of horizontal forces = 0, and net torque = 0.
C) Net torque = 0 only.
D) Sum of vertical forces = 0 only.
11. A system of concurrent forces is in equilibrium. If the forces are represented by vectors, their vector sum must be:
A) A non-zero scalar
B) A non-zero vector
C) The zero vector
D) Infinite
12. If a particle is in equilibrium, and one of the forces acting on it is removed, the remaining forces will have a resultant equal to:
A) Zero
B) The removed force
C) The negative of the removed force
D) The sum of the remaining forces
13. A body is in equilibrium. This implies that the net external force acting on it is:
A) Always zero.
B) Zero if the body is at rest.
C) Zero if the body is moving with constant velocity.
D) Always zero, regardless of its motion.
14. In Lami's Theorem, if two forces are perpendicular to each other, and the third force makes an angle θ with one of them, what is the relation between the forces?
A) F1/sin(90+θ) = F2/sin(θ) = F3/sin(90)
B) F1/sin(θ) = F2/sin(90+θ) = F3/sin(90)
C) F1/sin(90) = F2/sin(θ) = F3/sin(90+θ)
D) F1/sin(90) = F2/sin(90+θ) = F3/sin(θ)
15. A particle is acted upon by three forces: 3 N along the positive x-axis, 4 N along the positive y-axis, and F N along the negative x-axis. For equilibrium, what is the magnitude and direction of F?
A) 3 N along the negative x-axis
B) 3 N along the positive x-axis
C) 4 N along the negative y-axis
D) 7 N along the negative x-axis
16. If a system of concurrent forces is in equilibrium, then the work done by these forces when the point of application undergoes a small displacement is:
A) Positive
B) Negative
C) Zero
D) Infinite
17. Three forces P, Q, and R are acting at a point. For equilibrium, the resultant of P and Q must be equal and opposite to:
A) P
B) Q
C) R
D) P + Q
18. Consider a body in equilibrium. If a new force is added to the system, for the body to remain in equilibrium, the new force must be:
A) Equal to the resultant of the original forces.
B) Opposite to the resultant of the original forces.
C) Zero.
D) Equal to zero and opposite to the resultant of the original forces.
19. If a system of concurrent forces is in equilibrium, what is the net change in momentum of a particle acted upon by these forces over any time interval?
A) Maximum
B) Minimum
C) Zero
D) Equal to the net force
20. In Lami's theorem, if the angles between the forces are 90°, 120°, and 150°, what is the ratio of the magnitudes of the forces?
A) 1 : √3 : 2
B) 1 : 2 : √3
C) 2 : √3 : 1
D) √3 : 1 : 2
21. A particle is subjected to two forces, 5 N and 3 N. Can the particle be in equilibrium?
A) Yes, if they are in the same direction.
B) Yes, if they are in opposite directions and equal.
C) Yes, if they are perpendicular.
D) No, never.
22. If the resultant of a system of concurrent forces is zero, the system is said to be in:
A) Unstable equilibrium
B) Neutral equilibrium
C) Equilibrium
D) Rotational equilibrium
23. A weight of 10 N is suspended by two strings making angles 30° and 60° with the vertical. What are the tensions in the strings if the system is in equilibrium?
A) 10 N and 10 N
B) 5 N and 5 N
C) 10 N and 5 N
D) Cannot be determined without more information.
24. What is the condition for a system of concurrent forces to be in equilibrium in terms of components?
A) Sum of components along x-axis = 0, y-axis = 0, z-axis = 0.
B) Sum of magnitudes = 0.
C) Sum of components along x-axis = 0, y-axis = 0.
D) Sum of components along x-axis = 0, z-axis = 0.
25. If a particle is in equilibrium under the action of forces F1 and F2, then F1 = ?
A) F2
B) -F2
C) 0
D) 2*F2
26. In Lami's Theorem, the angles α, β, and γ are measured between:
A) The lines of action of the forces.
B) The resultant of the forces.
C) The perpendicular to the forces.
D) The direction of motion.
27. A body is acted upon by three forces. If the body is in equilibrium, it means that the body is:
A) At rest or moving with constant velocity.
B) At rest only.
C) Accelerating uniformly.
D) Experiencing no forces.
28. If three non-coplanar concurrent forces are in equilibrium, what can be said about their vector sum?
A) It is maximum.
B) It is minimum.
C) It is zero.
D) It is equal to the magnitude of the largest force.
29. Which of the following is a necessary condition for a particle to be in equilibrium?
A) Net force is zero.
B) Net torque is zero.
C) Net work done is zero.
D) Net impulse is zero.
30. A lamp is suspended by means of a string. The forces acting on the lamp are its weight and the tension in the string. For the lamp to be in equilibrium, the tension must be:
A) Greater than the weight and acting upwards.
B) Equal to the weight and acting upwards.
C) Less than the weight and acting upwards.
D) Equal to the weight and acting downwards.
31. Consider a system of forces in equilibrium. If we resolve all forces along any arbitrary axis, the algebraic sum of their components along that axis will be:
A) Maximum
B) Minimum
C) Zero
D) Equal to the resultant force
32. If two concurrent forces are acting on a body, for equilibrium, they must be:
A) Equal in magnitude and direction.
B) Equal in magnitude and opposite in direction.
C) Different in magnitude and opposite in direction.
D) Different in magnitude and direction.
33. A system of forces is in equilibrium. If we remove one of the forces, the system will:
A) Remain in equilibrium.
B) No longer be in equilibrium.
C) Start rotating.
D) Accelerate indefinitely.
34. In the context of equilibrium of concurrent forces, what does 'concurrent' imply?
A) The forces act along the same line.
B) The forces act at the same point.
C) The forces are equal in magnitude.
D) The forces are opposite in direction.
35. If a particle is subjected to forces F1, F2, and F3, and it is in equilibrium, then F1 + F2 + F3 = ?
A) F1
B) F2
C) F3
D) 0 (zero vector)
36. Three concurrent forces of magnitudes 5 N, 12 N, and 13 N are acting on a particle. If the particle is in equilibrium, what can be concluded?
A) The forces are collinear.
B) The forces are perpendicular to each other.
C) The forces form a right-angled triangle.
D) The sum of any two forces equals the third.
37. A sign is hung from a pole by two ropes. The weight of the sign acts downwards. The tensions in the two ropes are concurrent forces. For the sign to be in equilibrium, the vector sum of the tensions and the weight must be:
A) Equal to the sum of tensions
B) Equal to the weight
C) Zero
D) Non-zero
38. If a body is in equilibrium, its acceleration is:
A) Maximum
B) Minimum
C) Zero
D) Constant but non-zero
39. Consider a particle at rest. If it is subjected to two forces, what must be true for it to remain at rest?
A) The forces must be equal in magnitude and opposite in direction.
B) The forces must be perpendicular to each other.
C) The forces must be parallel.
D) The sum of the forces must be equal to the particle's mass.
40. Which principle states that if a body is in equilibrium under the action of three forces, then each force is proportional to the sine of the angle between the other two?
A) Newton's First Law
B) Newton's Second Law
C) Lami's Theorem
D) Principle of Superposition
41. A block is resting on a horizontal surface. The forces acting on it are its weight, the normal reaction from the surface, and possibly other forces. For the block to be in equilibrium, the vector sum of all these forces must be:
A) Equal to its mass
B) Equal to its weight
C) Zero
D) Non-zero
42. If a system of concurrent forces is in equilibrium, the resultant force is:
A) Maximum
B) Minimum
C) Zero
D) Infinite
43. A body is acted upon by three concurrent forces of magnitudes 3 N, 4 N, and 5 N. If the body is in equilibrium, what can be said about the angles between these forces?
A) The angles are arbitrary.
B) The forces must be parallel.
C) The forces form a right-angled triangle.
D) The forces must be perpendicular to each other.
44. Consider three concurrent forces in equilibrium. If one force is doubled, what must happen to the other forces to maintain equilibrium?
A) They must remain unchanged.
B) Their directions must change.
C) Their magnitudes and/or directions must change.
D) They can be removed.
45. In Lami's Theorem, what do α, β, and γ represent?
A) The angles between the forces themselves.
B) The angles opposite to the forces.
C) The angles adjacent to the forces.
D) The angles made by the forces with the horizontal.
46. According to Lami's Theorem, if three concurrent forces P, Q, and R are in equilibrium, then which relation holds true?
A) P/sin(α) = Q/sin(β) = R/sin(γ)
B) P/sin(α) = Q/sin(β) = R/sin(δ)
C) P/sin(β) = Q/sin(α) = R/sin(γ)
D) P/sin(γ) = Q/sin(β) = R/sin(α)
47. Lami's Theorem applies to a system of concurrent forces in equilibrium. What is the minimum number of concurrent forces required for Lami's Theorem to be applicable?
A) Two
B) Three
C) Four
D) Five
48. If three concurrent forces P, Q, and R are in equilibrium, which of the following statements is true?
A) P + Q + R = 0
B) P² + Q² + R² = 0
C) The magnitude of P + Q is equal to the magnitude of R.
D) The vector sum P + Q + R = 0.
49. What is the condition for a system of concurrent forces to be in equilibrium?
A) The vector sum of all forces acting on the system is zero.
B) The algebraic sum of all forces acting on the system is zero.
C) The resultant force is equal to the mass of the system.
D) The net torque acting on the system is zero.
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