If the given forces P1, P2, P3 and P4 are such that the force polygon does not close, then the system will A. Be in equilibrium B. Always reduce to a resultant force C. Always reduce to a couple D. Both (A) and (C)

Be in equilibrium
Always reduce to a resultant force
Always reduce to a couple
Both (A) and (C)

The correct answer is: C. Always reduce to a couple.

A force polygon is a graphical representation of the forces acting on a body. The forces are represented by arrows, and the sum of the forces is represented by the closing line of the polygon. If the force polygon does not close, then the system is not in equilibrium and will always reduce to a couple.

A couple is a pair of equal and opposite forces that act on a body at different points. The couple produces a torque, which is a rotational force. The torque of a couple is equal to the product of the magnitude of the forces and the distance between the points of action.

If the force polygon does not close, then the system is not in equilibrium. This means that the sum of the forces acting on the body is not zero. The only way to have a non-zero sum of forces and still be in equilibrium is if the forces are acting at different points. This is the case for a couple.

Therefore, if the force polygon does not close, then the system will always reduce to a couple.