Take Class 11 Tuition from the Best Tutors
Affordable fees 1-1 or Group class Flexible Timings Verified Tutors Search in
The moment of inertia of a body about a given axis is 1.2kgm^2 . Initially the body is at rest. In order to produce a rotational kinetic energy of 1500J, an angular acceleration of 25rad/second ^2 must be applied about that axis for a duration of
Asked by Abu Ashraf Last Modified
Answer 
The correct option is B 2 s
I=1.2 kgm2;t=?
Krot=1500 J
α=25rad/s2
ω=ω0+αt
Initially the body was at rest, ωo=0
Rotational kinetic energy, K=12Iω2⇒1500=12×1.2×w2
w=√30001.2=50 rad/s
ω=ω0+αt
ωo=0
t=wα=5025=2s
Rotation kinetic energy= ½Iω²
Where I = moment of Inertia
ω = angular velocity
And, kinematic relation for constant angular acceleration is
ω(final) = ω(initial) + αt
Where, α = angular acceleration
t = time
To find the duration for which an angular acceleration must be applied to produce a certain rotational kinetic energy, we can use the following relationship between rotational kinetic energy (KE), moment of inertia (I), and angular velocity (ω):
KE = \frac{1}{2} I \omega^2KE=21Iω2
Given that the rotational kinetic energy (KE) is 1500 J and the moment of inertia (I) is 1.2 kgm², we can solve for the angular velocity (ω):
1500 = \frac{1}{2} \times 1.2 \times \omega^21500=21×1.2×ω2
Solving for ω gives us:
\omega^2 = \frac{3000}{1.2}ω2=1.23000
\omega = \sqrt{\frac{3000}{1.2}}ω=1.23000
\omega \approx 50 \text{ rad/s}ω≈50 rad/s
Now, using the angular acceleration (α) of 25 rad/s², we can find the time (t) it takes to reach this angular velocity from rest using the equation:
\omega = \alpha tω=αt
Substituting the known values:
50 = 25t50=25t
t = \frac{50}{25}t=2550
t = 2 \text{ seconds}t=2 seconds
Therefore, an angular acceleration of 25 rad/s² must be applied about that axis for a duration of 2 seconds to produce a rotational kinetic energy of 1500 J.
View 10 more Answers
Related Questions
Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com
Ask a QuestionRelated Lessons
Recommended Articles
Science, Arts Or Commerce - Which One To Go For?
Once over with the tenth board exams, a heavy percentage of students remain confused between the three academic streams they have to choose from - science, arts or commerce. Some are confident enough to take a call on this much in advance. But there is no worry if as a student you take time to make choice between - science,...
Read full article >
How To Choose The Right School For Children?
Quality education does not only help children to get a successful career and life, but it also hugely contributes to society. The formal education of every child starts from school. Although there are numerous schools, parents find it challenging to choose the right one that would fit their child. It is difficult for them...
Read full article >
The Trend of E-learning and it’s Benefits
E-learning is not just about delivering lessons online. It has a much broader scope that goes beyond manual paper or PowerPoint Presentations. To understand the reach of E-learning and how the whole process works in developing the Educational system, we will discuss a few points here. Let us find out how this new learning...
Read full article >
Top Benefits of e-Learning
With the current trend of the world going digital, electronic renaissance is a new movement that is welcomed by the new generation as it helps makes the lives of millions of people easier and convenient. Along with this rapidly changing movement and gaining popularity of Internet, e-Learning is a new tool that emerging...
Read full article >
Looking for Class 11 Tuition ?
Learn from the Best Tutors on UrbanPro
Are you a Tutor or Training Institute?
Join UrbanPro Today to find students near youThe best tutors for Class 11 Tuition Classes are on UrbanPro
The best Tutors for Class 11 Tuition Classes are on UrbanPro
5
