If in a planar system only 2 reaction forces are acting, then the system is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 27/01/2018 (Evening)
Detailed Explanation
A rigid body in a plane has three degrees of freedom: x, y and rotation. To stop all three under any loading we need at least three independent reactions (not all concurrent and not all parallel).
Why “Essentially unstable” Is Correct
With only two reactions, there are three equilibrium equations but only two unknowns. For a general load, one of the equations cannot be satisfied, and the body moves. Such a body is partially constrained and therefore essentially unstable — option (a).
Disputed answer: the commission's revised key accepted (c) ‘Can't say’, perhaps because a particular load (for example one passing through the point where the two reactions meet) could still be balanced. But stability means resisting any load, and with two reactions that is impossible. The theoretically correct answer is (a).
| Case | Reactions vs equations (3 in a plane) | Result |
|---|---|---|
| Partially constrained | Fewer reactions than equations (< 3) | Unstable — the body can move |
| Improperly constrained | Enough reactions (≥ 3) but all concurrent or all parallel | Unstable — the body can rotate or slide |
| Properly constrained, determinate | 3 reactions, not concurrent, not parallel | Stable; statics gives all reactions |
| Properly constrained, indeterminate | More than 3 reactions | Stable; extra equations needed |
Why the Other Options Are Wrong
- B. Essentially stable: Two reactions cannot resist every possible load in a plane.
- C. Can't say: Accepted by the revised key, but theory gives a definite answer: with fewer than 3 reactions the body is unstable.
- D. None of these: The correct description, essentially unstable, is listed.
Key Point
Planar body: fewer than 3 reactions → partially constrained → unstable.
Key Concepts for Students
- Number of reactions ≥ 3 is necessary but not sufficient for stability.
- Reactions must not be all concurrent or all parallel.
- A mechanism is a structure with too few constraints.
Practice more: this is question 6 in Force Analysis MCQs – Part 1. Try the whole set and check every answer instantly.