If all the reactions acting on a planar system are concurrent, then the system is:

Asked in SSC JE 29/01/2018 (Morning)

Detailed Explanation

For a body in a plane to be held in place, its reactions must be able to resist movement in x, in y, and rotation. The arrangement of the reactions matters, not just their number.

Why “Essentially unstable” Is Correct

If all reactions are concurrent (their lines of action meet at one point), each has zero moment about that point. Any load whose line of action does not pass through that point creates a moment that the reactions cannot balance, so the body rotates about the point. Such a system is essentially (geometrically) unstable, however many reactions there are.

Force systems in a plane. Concurrent: lines of action meet at one point — such forces cannot produce a moment about that point. Parallel: lines of action are parallel — such forces cannot resist anything at right angles to them. Non-concurrent, non-parallel: the general case. A set of reactions that is all concurrent or all parallel cannot hold a body in every direction, so the body is improperly constrained.

Why the Other Options Are Wrong

A. Can't say: The outcome is certain — concurrent reactions always allow rotation.
B. Essentially stable: Stability needs the reactions to resist rotation, which concurrent ones cannot.
D. None of these: The correct description, essentially unstable, is listed.

Key Point

All reactions concurrent → cannot resist moment → unstable (improperly constrained).

Key Concepts for Students

All reactions parallel → cannot resist force at right angles → also unstable.
Three non-concurrent, non-parallel reactions give a stable, determinate planar body.
This is called geometric instability.

Practice more: this is question 3 in Force Analysis MCQs – Part 1. Try the whole set and check every answer instantly.