Equilibrium of a Body

When a body is in equilibrium, it means that the net force acting on the body is zero. This occurs when the vector sum of all the forces acting on the body is equal to zero.

Concurrent Forces

Concurrent forces are forces that act on a common point but have different lines of action. In other words, they intersect at a single point. When a body is subjected to three concurrent forces, it can be in equilibrium if certain conditions are met.

Resultant of Two Forces

The resultant of two forces is the vector sum of the two forces. In the case of concurrent forces, the resultant of any two forces can be determined by using the parallelogram law of vector addition.

Options a, b, c, and d

Option a: The resultant of any two forces is equal to the third force. This statement is not true because the resultant of two forces can have a magnitude and direction different from the third force.

Option b: The resultant of any two forces is opposite to the third force. This statement is also not true because the resultant can be in any direction depending on the magnitudes and directions of the individual forces.

Option c: The resultant of any two forces is collinear with the third force. This statement is not true either because the resultant can have a different direction from the third force.

Option d: All of these. This is the correct answer because it encompasses all the possibilities. The resultant of any two forces can be equal to the third force, opposite to the third force, or collinear with the third force, depending on the specific magnitudes and directions of the forces involved.

Conclusion

In summary, when a body is subjected to three concurrent forces and is in equilibrium, the resultant of any two forces can have various relationships with the third force. It can be equal to the third force, opposite to the third force, or collinear with the third force. Therefore, option d, "all of these," is the correct answer.