When three coplanar and non-parallel forces are in equilibrium,
I. they can be represented in magnitude and direction by the three sides of a triangle taken in order.
II. their lines of action meet at a point.
III. the magnitude of anyone equals the magnitude of the resultant of the other two.
IV. any one force is the equilibrant of the other two.
Which of the following statements above are correct?
I & II only
II & III only
II, III & IV only
I, II, III & IV
I, III & IV only
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For three coplanar and non-parallel forces to be in equilibrium, the following conditions must be satisfied:
1. Triangle Law of Forces (Statement I):
If three forces are in equilibrium, they can be represented in magnitude and direction by the three sides of a triangle taken in order.
This is a well-known result in statics.
2. Concurrent Forces (Statement II):
The lines of action of the three forces must meet at a single point (i.e., they must be concurrent) for equilibrium to exist.
3. Resultant of Two Forces (Statement III):
In equilibrium, the resultant of any two forces must be equal in magnitude but opposite in direction to the third force.
4. Equilibrant Force (Statement IV):
Any one of the three forces is the equilibrant of the other two, as it counterbalances their resultant.
Since all four statements are correct, the correct answer is:
D. I, II, III & IV
If a body is in equilibrium under the action of three non-parallel coplanar forces, the forces must be concurrent, that is, must meet at a single point. THE ANSWER IS C
