In which case does a plane lamina's center of gravity not coincide with its geometric center__________________?
Show answer Hide answer
Answer: A. right angled triangle
Explanation
A right-angled triangle's geometric center does not coincide with its centroid in the same manner as symmetrical shapes like squares or circles. The asymmetrical mass distribution of a right-angled triangle shifts its center of gravity away from its median intersection point. Calculating the centroid requires integrating area moments, which yields coordinates located one-third of the base and height from the orthogonal sides. The geometric center of a symmetrical shape like a circle or square aligns perfectly with its physical center of gravity. For a right-angled triangle, the centroid coordinates are located at one-third of the base width and one-third of the height. Asymmetrical lamina shapes lack point symmetry, causing their centroids to be offset from their bounding box geometric centers.
An equilateral triangle possesses three-fold rotational symmetry, causing its geometric center and centroid to coincide perfectly. A square is fully symmetrical across multiple axes, ensuring its geometric center and center of gravity are identical. A circle features infinite lines of symmetry, making its geometric center and centroid match exactly at the origin.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
Related questions
Q1. What is the proof resilience per unit volume of a material known as________________?
Show answer Hide answer
Answer: C. modulus of resilience
Proof resilience refers to the maximum strain energy stored in a material up to its elastic limit. Dividing this total stored energy by the volume of the material yields the modulus of resilience. This specific volumetri...
Q2. Which of the following serves as an illustration of a first-class lever__________________?
Show answer Hide answer
Answer: D. all of the above
A first class lever requires the fulcrum to be located directly between the applied effort and the load. Human arm movements feature the elbow joint serving as a fulcrum between muscle insertion and hand loads. Scissors...
Q3. What does it signify when a structural member is described as elastic under applied loads________________?
Show answer Hide answer
Answer: C. stretch
An elastic structural member deforms and stretches under applied loads while retaining the ability to spring back entirely. Elastic behavior means that atomic bonds stretch temporarily without suffering permanent displac...
Q4. How is Young’s modulus formulated as a ratio of mechanical properties___________________?
Show answer Hide answer
Answer: C. longitudinal stress and longitudinal strain
Young modulus quantifies the resistance of a material to longitudinal elastic deformation under load. It is mathematically formulated as the direct ratio of longitudinal stress to corresponding longitudinal strain. This...
Q5. What operational problems are caused by sulfur impurities in coal___________________?
Show answer Hide answer
Answer: E. all of the above
Sulfur content in coal reacts during combustion to form corrosive chemical compounds and low-melting slag deposits. Acidic sulfur dioxide gases condense at lower temperatures, leading to severe cold-end corrosion in down...
Q6. What is the standard value of Poisson’s ratio for cast iron_________________?
Show answer Hide answer
Answer: B. 0.23 to 0.27
The standard Poisson ratio for cast iron typically ranges between zero point two three and zero point two seven. This material constant reflects the specific volumetric and lateral strain relationships exhibited by gray...