EIT Statics 5 — Questions and Answers
Question 1: Varignon's theorem states that the moment of a resultant force about a point equals:
- The sum of moments of the component forces about the same point (Correct answer)
- The product of the resultant and the perpendicular distance to each component
- The cross product of each component with the position vector
- The vector sum of all force magnitudes
Correct answer: The sum of moments of the component forces about the same point
Varignon's theorem states that M_resultant = ΣM_components about the same point, simplifying moment calculations.
Question 2: The centroid of a composite area is found by:
- ΣAᵢx̄ᵢ / ΣAᵢ (Correct answer)
- ΣAᵢ / Σx̄ᵢ
- Σx̄ᵢ / n
- ΣAᵢx̄ᵢ
Correct answer: ΣAᵢx̄ᵢ / ΣAᵢ
The x-coordinate of the centroid of a composite area is x̄ = ΣAᵢx̄ᵢ / ΣAᵢ, the area-weighted average of component centroids.
Question 3: A particle is in equilibrium under the action of three concurrent forces. If two forces are 40 N and 30 N at right angles to each other, what is the magnitude of the third force?
- 50 N (Correct answer)
- 70 N
- 10 N
- 35 N
Correct answer: 50 N
The resultant of 40 N and 30 N is √(40² + 30²) = √2500 = 50 N; for equilibrium the third force must be 50 N in the opposite direction.
Question 4: The parallel axis theorem states that I = Ī + Ad². Here, Ī is the:
- Centroidal moment of inertia (Correct answer)
- Polar moment of inertia
- Moment of inertia about the base
- Product of inertia
Correct answer: Centroidal moment of inertia
In the parallel axis theorem, Ī is the moment of inertia about the centroidal axis parallel to the axis of interest.
Question 5: A 10 kN force acts along the line from A(0,0,0) to B(3,4,0) m. What is the unit vector along AB?
- (0.6i + 0.8j) (Correct answer)
- (3i + 4j)
- (0.75i + j)
- (0.5i + 0.5j)
Correct answer: (0.6i + 0.8j)
|AB| = √(3² + 4²) = 5 m; unit vector = (3i + 4j)/5 = 0.6i + 0.8j.
Question 6: In a statically determinate beam, the number of unknowns must equal the number of available equilibrium equations. For a 2D beam, how many equilibrium equations are available?
- 3 (Correct answer)
- 2
- 4
- 6
Correct answer: 3
In 2D statics, three equilibrium equations are available: ΣFx = 0, ΣFy = 0, and ΣM = 0.
Question 7: A cable supports a 500 N load and makes angles of 30° and 45° with the horizontal on its two segments. What is the tension in the 30° segment?
- 366 N (Correct answer)
- 500 N
- 259 N
- 433 N
Correct answer: 366 N
At the junction: T1 sin30° + T2 sin45° = 500 and T1 cos30° = T2 cos45°; solving: T1 = 500 cos45°/(sin30° cos45° + sin45° cos30°) = 500(0.707)/(0.5×0.707 + 0.707×0.866) = 353.5/(0.354 + 0.612) = 353.5/0.966 ≈ 366 N.
EIT Statics 5
Varignon's theorem states that the moment of a resultant force about a point equals: