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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?
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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.
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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
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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?
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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?.
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