If a system has more equations of equilibrium than the number of forces (reactions), then the system is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 22/01/2018 (Morning)
Detailed Explanation
Stability depends on comparing the number of unknown reactions with the number of equations of equilibrium (3 in a plane), and on how the reactions are arranged.
Why “Partially constrained” Is Correct
When there are fewer reactions than equations, not all the equations can be satisfied for a general load. Some movement is not restrained at all. This is called being partially constrained. (Improper constraint is the different case where the count is enough but the arrangement is wrong.)
| 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
- A. Improperly constrained: Improper constraint means enough reactions but badly arranged (parallel or concurrent).
- C. Stable: With too few reactions the body is not stable.
- D. None of these: Partially constrained is the correct term and is listed.
Key Point
Reactions < equations → partially constrained. Enough reactions but parallel/concurrent → improperly constrained.
Key Concepts for Students
- Reactions = equations and well arranged → statically determinate.
- Reactions > equations → statically indeterminate.
- Both partial and improper constraint make a structure unstable.
Practice more: this is question 8 in Force Analysis MCQs – Part 1. Try the whole set and check every answer instantly.