Mechanical Engineering Exam > Mechanical Engineering Questions > The area moment of inertia of a square of siz...
Start Learning for Free
The area moment of inertia of a square of size 1 unit about is diagonal is
- a)1/3
- b)1/4
- c)1/12
- d)1/6
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The area moment of inertia of a square of size 1 unit about is diagona...
For a square of side a, the area moment of inertia of square with respect to one diagonal is 
Here a = 1
Most Upvoted Answer
The area moment of inertia of a square of size 1 unit about is diagona...
The area moment of inertia, also known as the second moment of area or the moment of inertia of an area, is a property of a shape that measures its resistance to bending. It is a fundamental concept used in structural analysis and design.
To calculate the area moment of inertia of a square about its diagonal, we can consider the square as two isosceles right triangles joined together along their hypotenuses.
Let's consider the square with sides of length 1 unit. The diagonal of the square divides it into two congruent right triangles. Each triangle has a base and height of 1 unit.
The formula for the area moment of inertia of a right triangle about its base is given by:
I_base = (base^3 * height) / 36
Since both triangles are congruent, the total area moment of inertia of the square about its diagonal can be calculated as the sum of the individual area moments of inertia of the two triangles.
Total I = 2 * I_base
Calculating the area moment of inertia for one triangle:
I_base = (1^3 * 1) / 36
= 1 / 36
Multiplying by 2 to account for both triangles:
Total I = 2 * (1 / 36)
= 1 / 18
Therefore, the area moment of inertia of a square of size 1 unit about its diagonal is 1/18.
However, in the given options, none of them match the correct answer. The correct answer should be 1/18 and not 1/12 as mentioned in option 'C'.
To calculate the area moment of inertia of a square about its diagonal, we can consider the square as two isosceles right triangles joined together along their hypotenuses.
Let's consider the square with sides of length 1 unit. The diagonal of the square divides it into two congruent right triangles. Each triangle has a base and height of 1 unit.
The formula for the area moment of inertia of a right triangle about its base is given by:
I_base = (base^3 * height) / 36
Since both triangles are congruent, the total area moment of inertia of the square about its diagonal can be calculated as the sum of the individual area moments of inertia of the two triangles.
Total I = 2 * I_base
Calculating the area moment of inertia for one triangle:
I_base = (1^3 * 1) / 36
= 1 / 36
Multiplying by 2 to account for both triangles:
Total I = 2 * (1 / 36)
= 1 / 18
Therefore, the area moment of inertia of a square of size 1 unit about its diagonal is 1/18.
However, in the given options, none of them match the correct answer. The correct answer should be 1/18 and not 1/12 as mentioned in option 'C'.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer?
Question Description
The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer?.
The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer?.
Solutions for The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The area moment of inertia of a square of size 1 unit about is diagonal isa)1/3b)1/4c)1/12d)1/6Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup