Question

A body subjected to three concurrent forces is found to be in equilibrium. The resultant of any two forces will be.
A. Is equal to third force
B. Is opposite to third force
C. Is collinear with third force
D. All of these

Answer 1

As we know if a body needs to be in equilibrium that is stable equilibrium then the net forces on the particle should be zero that is if a force acting on the particle in left direction then to make it in equilibrium other force should act in right direction.

Complete step by step answer:
As in this question we are given with three concurrent, these are acting on a body, we know if there are two concurrent forces acting on a body then to make it in a equilibrium then these forces should act in opposite direction so in these three concurrent forces if the body needs to be in equilibrium then the resultant forces of two of them should be opposite to third force and should be equal to third force. Example if we are having three concurrent equal forces acting on a body and two of them are acting at $60^\circ$angle and third force is acting opposite to them then we know resultant of two vectors at $60^\circ$angle to each other is same as one of the vector but direction is in between them. So similarly in this question the resultant of two of them should be opposite to the third so that the body can remain in equilibrium.
Therefore the resultant of any two out of three concurrent forces should be equal in magnitude to the third one, opposite to the direction of the third one and collinear with the third one.
Hence the correct option is D) All of the above

Note: As we know resultant of two them should be opposite to third that is as we have discussed in example above that if two are acting at $60^\circ$angle to each other then resultant will be opposite to third, collinear to third and equal to third. It can also be done if the angle is not $60^\circ$but then the value of force will also change.