JEE Exam > JEE Questions > The moment of inertia of a body about a given...
Start Learning for Free
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2 must be applied about that axis for a duration of :
Correct answer is '2'. Can you explain this answer?
Most Upvoted Answer
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initi...
Free Test
FREE
| Start Free Test |
Community Answer
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initi...
Solution:
Given:
Moment of inertia (I) = 1.2 kg-m^2
Rotational kinetic energy (KE) = 1500 J
Angular acceleration (α) = 25 rad/s^2
We need to find the duration for which the angular acceleration must be applied in order to produce the given rotational kinetic energy.
- To find the duration, we can use the equation for rotational kinetic energy:
KE = 1/2 * I * ω^2
where ω is the angular velocity.
- We can rearrange this equation to solve for ω:
ω^2 = 2 * KE / I
ω = √(2 * KE / I)
- Now, we know that angular acceleration is the rate of change of angular velocity. So, we can relate angular acceleration (α) and angular velocity (ω) using the equation:
ω = α * t
where t is the time duration for which the angular acceleration is applied.
- Substituting the value of ω from the previous equation, we get:
α * t = √(2 * KE / I)
- Squaring both sides of the equation, we get:
α^2 * t^2 = 2 * KE / I
- Now, substituting the given values, we have:
25^2 * t^2 = 2 * 1500 / 1.2
625 * t^2 = 2500
t^2 = 2500 / 625
t^2 = 4
t = √4
t = 2
Hence, the duration for which the angular acceleration must be applied is 2 seconds.
Given:
Moment of inertia (I) = 1.2 kg-m^2
Rotational kinetic energy (KE) = 1500 J
Angular acceleration (α) = 25 rad/s^2
We need to find the duration for which the angular acceleration must be applied in order to produce the given rotational kinetic energy.
- To find the duration, we can use the equation for rotational kinetic energy:
KE = 1/2 * I * ω^2
where ω is the angular velocity.
- We can rearrange this equation to solve for ω:
ω^2 = 2 * KE / I
ω = √(2 * KE / I)
- Now, we know that angular acceleration is the rate of change of angular velocity. So, we can relate angular acceleration (α) and angular velocity (ω) using the equation:
ω = α * t
where t is the time duration for which the angular acceleration is applied.
- Substituting the value of ω from the previous equation, we get:
α * t = √(2 * KE / I)
- Squaring both sides of the equation, we get:
α^2 * t^2 = 2 * KE / I
- Now, substituting the given values, we have:
25^2 * t^2 = 2 * 1500 / 1.2
625 * t^2 = 2500
t^2 = 2500 / 625
t^2 = 4
t = √4
t = 2
Hence, the duration for which the angular acceleration must be applied is 2 seconds.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer?
Question Description
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer?.
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer?.
Solutions for The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. 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 The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer?, a detailed solution for The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer? has been provided alongside types of The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 J, an angular acceleration of 25 rad/s2must be applied about that axis for a duration of :Correct answer is '2'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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