**Answer to Provided MCQ:**
**Correct Option:** C) 3
**Justification:** In a general coplanar force system, all forces lie in the same plane but can act in any direction. For static equilibrium, three independent equations must be satisfied: the sum of forces in the x-direction equals zero (ΣFx = 0), the sum of forces in the y-direction equals zero (ΣFy = 0), and the sum of moments about any point equals zero (ΣM = 0). Therefore, a maximum of three unknown forces can be determined.
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### Additional High-Yield MCQs on Equilibrium & Static Determinacy
1. **In a co planar parallel force system, the number of unknown forces that can be found by the principle of statics ......**
a) 3
b) 2
c) 1
d) 0
**Correct Answer:** b) 2
2. **The number of independent equations to be satisfied for static equilibrium of a plane structure is ......**
a) 1
b) 2
c) 3
d) 6
**Correct Answer:** c) 3
3. **The number of independent equations to be satisfied for static equilibrium in a space structure is ......**
a) 2
b) 3
c) 4
d) 6
**Correct Answer:** d) 6
4. **What is the maximum number of unknown reaction components that can be determined using only statics?**
a) 0
b) 1
c) 2
d) 3
**Correct Answer:** d) 3
5. **If the beam is supported so that there are only three unknown reactive elements at the supports. These can be determined by using the following fundamental equation of statics ......**
a) ΣH = 0
b) ΣV = 0
c) ΣH = 0, ΣV = 0
d) ΣH = 0, ΣV = 0, ΣM = 0
**Correct Answer:** d) ΣH = 0, ΣV = 0, ΣM = 0
6. **For a beam, if fundamental equations of statics are not sufficient to determine all the reactive forces at the supports, the structure is said to be ......**
a) determinate
b) statically determinate
c) statically indeterminate
d) none of these
**Correct Answer:** c) statically indeterminate
7. **A beam is said to be in equilibrium if ......**
a) it moves horizontally
b) it moves vertically
c) it rotates about its CG
d) none of these
**Correct Answer:** d) none of these
8. **If two forces acting at a joint are not along the straight line, then for the equilibrium of the joint ......**
a) one of the forces must be zero
b) each force must be zero
c) forces must be equal and of the same sign
d) forces must be equal in magnitude but opposite in sign
**Correct Answer:** b) each force must be zero
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### Core Theoretical Concepts (General Coplanar Force System & Equilibrium)
- A general coplanar force system consists of forces that all lie in the same plane but can have any direction.
- For a body to be in static equilibrium, the net force and net moment acting on it must be zero.
- Three independent equations of equilibrium exist for a 2D (coplanar) system:
1. ΣFx = 0 (Sum of horizontal forces equals zero)
2. ΣFy = 0 (Sum of vertical forces equals zero)
3. ΣM = 0 (Sum of moments about any point equals zero)
- These three equations can be used to solve for a maximum of three unknown quantities (e.g., support reactions, internal forces).
- If the number of unknowns exceeds the number of available equilibrium equations, the structure is **statically indeterminate** and requires compatibility conditions for analysis.
- The choice of the point for taking moments is arbitrary; a strategically chosen point can simplify calculations by eliminating unknowns.
- For a **coplanar parallel force system** (a special case where all forces are parallel), the equilibrium equations reduce to two: ΣF (in the direction of forces) = 0 and ΣM = 0.
- For a 3D (space) structure, six equilibrium equations exist: ΣFx=0, ΣFy=0, ΣFz=0, ΣMx=0, ΣMy=0, ΣMz=0.
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