JEE Exam > JEE Questions > Let I be the moment of inertia of a uniform s...
Start Learning for Free
Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal to
- a)I
- b)I sin2θ
- c)I cos2θ
- d)I cos2 (θ/2)
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let I be the moment of inertia of a uniform square plate about an axis...
A'B' ⊥ AB and C' D'⊥ CD
From symmetry IAB = IA'B' and ICD = IC'D'
From theorem of
From theorem of
perpendicular axes,
Izz = IAB + IA'B' = ICD + IC'D'
⇒ 2IAB = 2ICD
∴ IAB = ICD
Most Upvoted Answer
Let I be the moment of inertia of a uniform square plate about an axis...
The moment of inertia of a uniform square plate about an axis passing through its center and parallel to two of its sides is given by the formula:
I = (1/6) * m * a^2
where m is the mass of the plate and a is the length of one side of the square.
To find the moment of inertia about the axis CD, we can use the parallel axis theorem. The parallel axis theorem states that the moment of inertia about an axis parallel to and at a distance d from an axis passing through the center of mass is given by:
I' = I + m * d^2
where I' is the moment of inertia about the new axis.
In this case, the distance between the axis AB and CD is a/2, since CD passes through the center of the plate. Therefore, we can substitute I and d into the parallel axis theorem equation:
I' = (1/6) * m * a^2 + m * (a/2)^2
= (1/6) * m * a^2 + (1/4) * m * a^2
= (1/6 + 1/4) * m * a^2
= (5/12) * m * a^2
Therefore, the moment of inertia of the plate about the axis CD is (5/12) * I, which is equal to option b) I * sin^2(q).
I = (1/6) * m * a^2
where m is the mass of the plate and a is the length of one side of the square.
To find the moment of inertia about the axis CD, we can use the parallel axis theorem. The parallel axis theorem states that the moment of inertia about an axis parallel to and at a distance d from an axis passing through the center of mass is given by:
I' = I + m * d^2
where I' is the moment of inertia about the new axis.
In this case, the distance between the axis AB and CD is a/2, since CD passes through the center of the plate. Therefore, we can substitute I and d into the parallel axis theorem equation:
I' = (1/6) * m * a^2 + m * (a/2)^2
= (1/6) * m * a^2 + (1/4) * m * a^2
= (1/6 + 1/4) * m * a^2
= (5/12) * m * a^2
Therefore, the moment of inertia of the plate about the axis CD is (5/12) * I, which is equal to option b) I * sin^2(q).
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer?
Question Description
Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer?.
Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer?.
Solutions for Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle q with AB. The moment of inertia of the plate about the axis CD is then equal toa)Ib)I sin2θc)I cos2θd)I cos2 (θ/2)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
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