Class 11 Exam > Class 11 Questions > A child is standing with folded hands at the ...
Start Learning for Free
A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is
[JEE'(Scr) 2004]
- a)2K
- b)K/2
- c)K/4
- d)4K
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A child is standing with folded hands at the centre of a platform rota...
To understand why the kinetic energy of the system becomes K/2 when the child stretches his arms, let's break down the problem step by step.
1. Initial Situation:
- Initially, the child is standing with folded hands at the center of a rotating platform.
- The platform is rotating about its central axis, which means it has angular velocity.
- The child's arms are close to the body, so the moment of inertia of the system is relatively small.
- The kinetic energy of the system is denoted as K.
2. Stretching Arms:
- When the child stretches his arms, the distribution of mass changes.
- The moment of inertia of the system depends on the mass distribution and the distance of the mass elements from the axis of rotation.
- By stretching his arms, the child increases the moment of inertia of the system, effectively doubling it.
3. Conservation of Angular Momentum:
- According to the law of conservation of angular momentum, the angular momentum of a system remains constant unless acted upon by an external torque.
- In this case, since no external torque is acting on the system, the angular momentum remains constant.
4. Relationship between Angular Momentum and Moment of Inertia:
- The angular momentum of a rotating system is given by the product of the moment of inertia and the angular velocity.
- Since the angular momentum is conserved, if the moment of inertia doubles, the angular velocity must halve.
5. Relationship between Kinetic Energy and Angular Velocity:
- The kinetic energy of a rotating system is given by the formula K = (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
- As the angular velocity decreases, the kinetic energy of the system also decreases.
- The relationship between kinetic energy and angular velocity is quadratic, so halving the angular velocity will result in the kinetic energy being halved as well.
Therefore, when the child stretches his arms, the moment of inertia of the system doubles, leading to the angular velocity halving. As a result, the kinetic energy of the system becomes K/2.
1. Initial Situation:
- Initially, the child is standing with folded hands at the center of a rotating platform.
- The platform is rotating about its central axis, which means it has angular velocity.
- The child's arms are close to the body, so the moment of inertia of the system is relatively small.
- The kinetic energy of the system is denoted as K.
2. Stretching Arms:
- When the child stretches his arms, the distribution of mass changes.
- The moment of inertia of the system depends on the mass distribution and the distance of the mass elements from the axis of rotation.
- By stretching his arms, the child increases the moment of inertia of the system, effectively doubling it.
3. Conservation of Angular Momentum:
- According to the law of conservation of angular momentum, the angular momentum of a system remains constant unless acted upon by an external torque.
- In this case, since no external torque is acting on the system, the angular momentum remains constant.
4. Relationship between Angular Momentum and Moment of Inertia:
- The angular momentum of a rotating system is given by the product of the moment of inertia and the angular velocity.
- Since the angular momentum is conserved, if the moment of inertia doubles, the angular velocity must halve.
5. Relationship between Kinetic Energy and Angular Velocity:
- The kinetic energy of a rotating system is given by the formula K = (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
- As the angular velocity decreases, the kinetic energy of the system also decreases.
- The relationship between kinetic energy and angular velocity is quadratic, so halving the angular velocity will result in the kinetic energy being halved as well.
Therefore, when the child stretches his arms, the moment of inertia of the system doubles, leading to the angular velocity halving. As a result, the kinetic energy of the system becomes K/2.
Free Test
FREE
| Start Free Test |
Community Answer
A child is standing with folded hands at the centre of a platform rota...
According to the principle of conservation of angular momentum,
Iω = constant
As I is doubled, w becomes half.
Now K.E. of rotation,
Since I is doubled and ω is halved, therefore
K.E. will become half i.e. k/2.
Iω = constant
As I is doubled, w becomes half.
Now K.E. of rotation,
Since I is doubled and ω is halved, therefore
K.E. will become half i.e. k/2.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer?
Question Description
A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer?.
A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is[JEE(Scr) 2004]a)2Kb)K/2c)K/4d)4KCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup