Lamis Theorem

Newton’s first law states that when a particle is in equilibrium, the total of the forces acting on it is zero. If a particle in equilibrium is subjected to only three coplanar, concurrent and non collinear forces, the vectors representing the three forces have a specific geometry, which is described by Lami’s theorem. Lami’s theorem states that if three forces acting at a point are in equilibrium, each force is directly proportional to the sine of the angle between the remaining two forces. It specifies the equilibrium requirements for three forces operating at a single place.

1.According to which of the following theories, “if a body is in equilibrium under the action of three coplanar and concurrent forces, each of the forces is proportional to the sine of the angle between the other two,” “if a body is in equilibrium under the action of three coplanar and concurrent forces, each of the forces is proportional to the sine of the angle between the other two”?

1. a) Parallelogram Law of Forces
2. b) Lami’s Theorem
3. c) Triangle Law of Forces
4. d) Polygon Law of Forces

Answer- b

2.What is the smallest number of non-zero vectors that may be joined in distinct planes to provide a consequence of zero?

1. a) Two
2. b) Three
3. c) Four
4. d) Five

Answer- c

3. Which of the following propositions is true according to Lami’s theorem?
4. a) At a given position, three opposing forces will be in balance.
5. b) If three forces operating on a particle are represented in magnitude and direction by the sides of a triangle in order, they will be in equilibrium.
6. c) When three forces operating at the same place are in equilibrium, each force is proportional to the sine of the angle formed by the other two.
7. d) A triangle may be used to depict three forces operating on a point, with each side proportionate to the force.

Answer- c, as each force is proportional to the sine of the angle between the other two if three forces operating at a place are in equilibrium.

4.Which of the following statements concerning Lami’s theorem is correct?

1. a) The theorem is obtained using trigonometry’s cosine rule.
2. b) The theorem only applies to bodies in equilibrium with regular shapes.
3. c) The theorem is useful for estimating the unknown forces operating on an item in equilibrium at a given position.
4. d) The force applied on a moving body is determined by the theorem.

Answer- c, as the theorem is useful in estimating the unknown forces operating on an item in equilibrium at a given place.

5. At a location in the plane, three coplanar forces A, B, and C are in equilibrium. What is the value of C if the supplied value of A is 1.9318 kg wt and sin1 is 0.9659?
6. a) 1
7. b) 2
8. c) 0.9659
9. d) ½

Answer- a 

7. If the body is in equilibrium due to a set of non-colinear forces, the minimal number of forces must be- 
8. a) Two
9. b) Three
10. c) Four
11. d) Five

Answer- b

8.A person’s weight is determined by-

1. a) Earth’s centripetal force
2. b) The earth’s gravitational force 

 c)Attraction force experienced by a person

 d)the gravitational pull towards the earth’s centre

 Answer- d

9.The result of either couple’s force and the couple’s arm are known as

1. a) couple as a consequence
2. b) the moment of inertia of the forces
3. c) the pair that emerges
4. d) the couple’s moment

Answer- d

10.In air, a metal sample weighs 219 grams, 180 grams in water, and 120 grams in an unknown fluid. So, which assertion concerning metal density is correct?

1. a) It is impossible to calculate the density of metal.
2. b) The density of B. metal is twice that of water.
3. c) In water, C. metal will float.
4. d) The density of D. metal is double that of the unknown fluid.

Answer- a

11.Coulomb friction is the friction between two surfaces-

1. a) bodies in motion relative to one another
2. b) two completely dry areas
3. c) lubricated surfaces on both sides

d)Solids and liquids

Answer- a

12.According to the force triangle rule-

1. a) At a given position, three forces will be in balance.
2. b) A triangle may be used to depict three forces operating on a point, with each side proportionate to the force.
3. c) If the magnitude and direction of three forces operating on a particle are represented by the sides of a triangle in order, they will be in equilibrium.
4. d) When three forces operating at the same place are in equilibrium, each force is proportional to the sine of the angle formed by the other two.

Answer- c

13. If a rigid body is in equilibrium under the action of three forces, then-
14. a) These forces are equal
15. b) These forces’ lines of action meet at a point.
16. c) These forces’ paths of operation are parallel.
17. d) (b) and (c) in the previous paragraphs

Answer- d

14.If two forces of magnitude P operate at right angles, their influence may be neutralised by a third force of magnitude P operating along their bisector in the opposite direction-

1. a) 2P
2. b) P/2
3. c) √2P 
4. d) P/√2

Answer- c

15.D’ Alembert’s concept is utilised for- 

1. a) Reducing the kinetics issue to an analogous statics problem 
2. b) Determining truss stresses 
3. c) Floating body stability 
4. d) Designing safe structures

Answer- a

16.A heavy ladder lying on the floor and against a vertical wall may not be in balance-

1. a) The floor is smooth and the wall is rough.
2. b) The floor is rough, whereas the wall is smooth. 
3. c) Both the floor and the wall have smooth surfaces.
4. d) Both the floor and the wall have a rough texture.

Answer- c

17.Lami’s theorem states that

1. a)  At a given position, three forces will be in balance.
2. b)  A triangle may be used to depict three forces operating on a point, with each side proportionate to the force.
3. c) If the magnitude and direction of three forces acting on a particle are represented by the sides of a triangle in sequence, they will be in equilibrium.
4. d) Each force is proportional to the sine of the angle between the other two if three forces operating at a place are in equilibrium. 

Answer- d 

18. The result of either couple’s force and the couple’s arm are known as-
19. a) Resultant couple
20. b) Force-moment
21. c) Combination of the two
22. d) The couple’s moment

Answer- d