**Answer to Provided MCQ:**
**Correct Option:** B) 2
**Justification:** In a coplanar parallel force system, all forces act in the same direction and lie in the same plane. The equilibrium equations reduce to: ΣF_y = 0 (sum of vertical forces) and ΣM = 0 (sum of moments). ΣF_x = 0 is automatically satisfied as there are no horizontal components. Therefore, only 2 equations are available to find unknowns.
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### Additional High-Yield MCQs on Equilibrium & Static Determinacy
1. **In a general co planar force system, the number of unknown forces that can be found by the principle of statics is ......**
a) 1
b) 2
c) 3
d) 0
**Correct Answer:** c) 3
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. **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
5. **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
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 force 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 (Equilibrium & Static Determinacy)
- A body is in static equilibrium when the resultant force and resultant moment about any point are zero.
- For a coplanar force system, three equilibrium equations exist: ΣFx = 0, ΣFy = 0, ΣM = 0.
- For a coplanar parallel force system (all forces parallel), only two equations are independent: ΣF (in force direction) = 0 and ΣM = 0.
- For a space structure, six equilibrium equations exist: three force sums (ΣFx, ΣFy, ΣFz) and three moment sums (ΣMx, ΣMy, ΣMz).
- A structure is statically determinate if all support reactions can be found using equilibrium equations alone.
- If unknowns exceed available equilibrium equations, the structure is statically indeterminate.
- The principle of statics can solve for a maximum of 3 unknowns in a 2D problem and 6 unknowns in a 3D problem.
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