Identify the incorrect assertion among the following choices _______________?
Show answer Hide answer
Answer: D. The C.G. of a semicircle is at a distance of r/2 from the center
Explanation
The center of gravity of a semicircle is located at a distance of 4r/(3π) from its center, making the r/2 statement incorrect. Geometric integration of semicircular area moments yields a centroid height slightly higher than half the radius. Symmetry places the horizontal center on the vertical axis, but the vertical coordinate requires calculus integration. Center of gravity is the average location of the weight distribution of a rigid geometric shape. Standard geometric centroids are tabulated in engineering handbooks for structural cross-section analysis. The radius of a circular arc or area determines the scaling factor for centroidal distance formulas.
Option A is correct because a circle's center of gravity lies precisely at its geometric center. Option B correctly places a triangle's centroid at the intersection of its three median lines. Option C correctly locates a rectangle's center at the crossing point of its diagonal lines.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
Related questions
Q1. How do theoretical, ideal machines perform________________?
Show answer Hide answer
Answer: B. mechanical advantage is equal to velocity ratio
Theoretical ideal machines have no energy losses, meaning their mechanical advantage perfectly equals their velocity ratio. Conservation of energy dictates that input work equals output work when friction and internal lo...
Q2. Which force term is omitted within the virtual work equation_______________?
Show answer Hide answer
Answer: D. all of the above
Ideal constraints do not perform mechanical work because their reactions are perpendicular to motion paths. Smooth contact surfaces exert forces normal to sliding directions resulting in zero displacement work. Fixed piv...
Q3. If three non-coplanar forces form the sides of a triangle, what equilibrium state do they achieve________________?
Show answer Hide answer
Answer: A. non-equilibrium
Three non-coplanar forces forming the sides of a triangle cannot form a closed balanced system in a single plane, resulting in non-equilibrium. Equilibrium of forces requires vector sums in three dimensional space to equ...
Q4. The algebraic summation of the scalar components of multiple forces along a fixed axis equals the component of their resultant along that same axis, according to the principle of__________________?
Show answer Hide answer
Answer: E. resolution of forces
The principle of resolution of forces states that the sum of scalar components of forces along an axis equals the component of their resultant along that axis. This principle allows complex multi-force systems to be brok...
Q5. What geometric curve approximates a heavy flexible cable suspended between identical horizontal elevations when its central sag is minimal___________________?
Show answer Hide answer
Answer: B. parabola
Uniformly distributed loads suspended across horizontal spans form parabolic curves. Cables carrying their own weight alone form catenaries while heavy uniform decks create parabolas. Approximating small sag conditions s...
Q6. When a rigid body achieves equilibrium under the action of a three-force system, what conditions apply_______________?
Show answer Hide answer
Answer: D. B. and C. above
A rigid body in equilibrium under a three-force system requires that the forces are either all parallel or their lines of action meet at a single point. Concurrent lines of action ensure that no net rotational moment is...