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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now is
- 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 aplatform rotat...
Understanding the Problem
A child is standing at the center of a rotating platform. Initially, the kinetic energy of the system is K. When the child stretches their arms, the moment of inertia of the system doubles.
Key Concepts
- Kinetic Energy (KE): The kinetic energy of a rotating system is given by the formula: KE = (1/2) * I * ω², where I is the moment of inertia and ω is the angular velocity.
- Moment of Inertia (I): It quantifies how much mass is distributed relative to the axis of rotation.
Initial Conditions
- Let I₁ be the initial moment of inertia.
- The initial kinetic energy is K = (1/2) * I₁ * ω₁².
After Stretching Arms
- When the child stretches their arms, the moment of inertia doubles: I₂ = 2 * I₁.
- Angular momentum (L) must be conserved in the absence of external torques: L = I * ω.
Conservation of Angular Momentum
- Initially: L₁ = I₁ * ω₁.
- After stretching arms: L₂ = I₂ * ω₂ = 2 * I₁ * ω₂.
- Setting L₁ = L₂ gives: I₁ * ω₁ = 2 * I₁ * ω₂.
- Simplifying, we find ω₂ = ω₁ / 2.
New Kinetic Energy Calculation
- The new kinetic energy K₂ is:
K₂ = (1/2) * I₂ * ω₂²
K₂ = (1/2) * (2 * I₁) * (ω₁ / 2)²
K₂ = (1/2) * (2 * I₁) * (ω₁² / 4)
K₂ = (1/4) * I₁ * ω₁² = K/2.
Conclusion
The new kinetic energy of the system after the child stretches their arms is K/2, which corresponds to option B.
A child is standing at the center of a rotating platform. Initially, the kinetic energy of the system is K. When the child stretches their arms, the moment of inertia of the system doubles.
Key Concepts
- Kinetic Energy (KE): The kinetic energy of a rotating system is given by the formula: KE = (1/2) * I * ω², where I is the moment of inertia and ω is the angular velocity.
- Moment of Inertia (I): It quantifies how much mass is distributed relative to the axis of rotation.
Initial Conditions
- Let I₁ be the initial moment of inertia.
- The initial kinetic energy is K = (1/2) * I₁ * ω₁².
After Stretching Arms
- When the child stretches their arms, the moment of inertia doubles: I₂ = 2 * I₁.
- Angular momentum (L) must be conserved in the absence of external torques: L = I * ω.
Conservation of Angular Momentum
- Initially: L₁ = I₁ * ω₁.
- After stretching arms: L₂ = I₂ * ω₂ = 2 * I₁ * ω₂.
- Setting L₁ = L₂ gives: I₁ * ω₁ = 2 * I₁ * ω₂.
- Simplifying, we find ω₂ = ω₁ / 2.
New Kinetic Energy Calculation
- The new kinetic energy K₂ is:
K₂ = (1/2) * I₂ * ω₂²
K₂ = (1/2) * (2 * I₁) * (ω₁ / 2)²
K₂ = (1/2) * (2 * I₁) * (ω₁² / 4)
K₂ = (1/4) * I₁ * ω₁² = K/2.
Conclusion
The new kinetic energy of the system after the child stretches their arms is K/2, which corresponds to option B.
Free Test
FREE
| Start Free Test |
Community Answer
A child is standing with folded hands at the centre of aplatform rotat...
You have to apply the formula k = L^2/2 I to get the answer
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
|
|
Top Courses for Class 11View all
A child is standing with folded hands at the centre of aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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 aplatform rotating about its central axis. The kineticenergy of the system is K. The child now stretches hisarms so that the moment of inertia of the systemdoubles. The kinetic energy of the system now isa)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