If ΣH and ΣV are the algebraic sums of the forces resolved horizontally and vertically, and ΣM is the algebraic sum of the moments of the forces about any point, then for equilibrium of the body:
Try it first: pick an option, then read the explanation.
Correct answer: D. All options are correct
Asked in SSC JE 04/03/2017 (Morning)
Detailed Explanation
A body in a plane can move in three independent ways: horizontally, vertically and by rotating. Each needs its own condition to be stopped.
Why “All options are correct” Is Correct
- ΣH = 0 — no net horizontal force, so no horizontal acceleration.
- ΣV = 0 — no net vertical force.
- ΣM = 0 about any point — no net turning effect.
All three are needed together, so the answer is (d).
| Force system (in a plane) | Conditions of equilibrium |
|---|---|
| Concurrent forces | ΣH = 0, ΣV = 0 |
| Parallel forces | ΣF = 0 (along the forces), ΣM = 0 |
| General (non-concurrent) forces | ΣH = 0, ΣV = 0, ΣM = 0 about any point |
Why the Other Options Are Wrong
- A. ΣH = 0: Needed, but not enough on its own.
- B. ΣV = 0: Needed, but not enough on its own.
- C. ΣM = 0: Needed, but not enough on its own.
Key Point
Coplanar equilibrium: ΣH = 0, ΣV = 0, ΣM = 0.
Key Concepts for Students
- Two moment equations plus one force equation can replace this set (if the points are chosen properly).
- For concurrent forces ΣM = 0 is automatically satisfied.
- These three equations limit a planar determinate body to 3 unknown reactions.
Practice more: this is question 2 in General Conditions of Equilibrium MCQs – Part 1. Try the whole set and check every answer instantly.