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A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected ?
[AIEEE 2004]
- a)Moment of inertia
- b)Angular momentum
- c)Angular velocity
- d)Rotational kinetic energy
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A solid sphere is rotating in free space. If the radius of the sphere ...
B.Angular momentum
In free space, neither acceleration due to gravity for external torque act on the rotating solid sphere. Therefore, taking the same mass of sphere if the radius is increased then a moment of inertia, rotational kinetic energy and angular velocity will change but according to the law of conservation of momentum, angular momentum will not change.
In free space, neither acceleration due to gravity for external torque act on the rotating solid sphere. Therefore, taking the same mass of sphere if the radius is increased then a moment of inertia, rotational kinetic energy and angular velocity will change but according to the law of conservation of momentum, angular momentum will not change.
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A solid sphere is rotating in free space. If the radius of the sphere ...
Moment of Inertia:
- Moment of inertia depends on the distribution of mass within a rotating object.
- When the radius of the sphere is increased while keeping the mass constant, the mass distribution changes.
- As a result, the moment of inertia will be affected and it will increase.
- Therefore, the moment of inertia will not remain the same if the radius of the sphere is increased.
Angular Velocity:
- Angular velocity is the rate at which an object rotates.
- The angular velocity of the sphere will remain the same even if the radius is increased.
- This is because the angular velocity depends on the time taken to complete one revolution, and increasing the radius does not affect the time taken for one revolution.
- Therefore, the angular velocity will not be affected if the radius of the sphere is increased.
Angular Momentum:
- Angular momentum is the product of moment of inertia and angular velocity.
- As mentioned earlier, the moment of inertia will increase if the radius of the sphere is increased.
- However, the angular velocity will remain constant.
- Therefore, the angular momentum will not be affected if the radius of the sphere is increased.
Rotational Kinetic Energy:
- Rotational kinetic energy depends on both the moment of inertia and the angular velocity.
- Since the moment of inertia will increase if the radius of the sphere is increased, and the angular velocity remains constant, the rotational kinetic energy will be affected.
- Therefore, the rotational kinetic energy will not remain the same if the radius of the sphere is increased.
Conclusion:
- Among the given options, only the angular momentum will not be affected if the radius of the sphere is increased while keeping the mass constant.
- The moment of inertia, angular velocity, and rotational kinetic energy will all be affected by the change in radius.
- Moment of inertia depends on the distribution of mass within a rotating object.
- When the radius of the sphere is increased while keeping the mass constant, the mass distribution changes.
- As a result, the moment of inertia will be affected and it will increase.
- Therefore, the moment of inertia will not remain the same if the radius of the sphere is increased.
Angular Velocity:
- Angular velocity is the rate at which an object rotates.
- The angular velocity of the sphere will remain the same even if the radius is increased.
- This is because the angular velocity depends on the time taken to complete one revolution, and increasing the radius does not affect the time taken for one revolution.
- Therefore, the angular velocity will not be affected if the radius of the sphere is increased.
Angular Momentum:
- Angular momentum is the product of moment of inertia and angular velocity.
- As mentioned earlier, the moment of inertia will increase if the radius of the sphere is increased.
- However, the angular velocity will remain constant.
- Therefore, the angular momentum will not be affected if the radius of the sphere is increased.
Rotational Kinetic Energy:
- Rotational kinetic energy depends on both the moment of inertia and the angular velocity.
- Since the moment of inertia will increase if the radius of the sphere is increased, and the angular velocity remains constant, the rotational kinetic energy will be affected.
- Therefore, the rotational kinetic energy will not remain the same if the radius of the sphere is increased.
Conclusion:
- Among the given options, only the angular momentum will not be affected if the radius of the sphere is increased while keeping the mass constant.
- The moment of inertia, angular velocity, and rotational kinetic energy will all be affected by the change in radius.
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A solid sphere is rotating in free space. If the radius of the sphere ...
In free space, neither acceleration due to gravity for external torque act on the rotating solid sphere. Therefore, taking the same mass of sphere if the radius is increased then a moment of inertia, rotational kinetic energy and angular velocity will change but according to the law of conservation of momentum, angular momentum will not change.
In free space, neither acceleration due to gravity for external torque act on the rotating solid sphere. Therefore, taking the same mass of sphere if the radius is increased then a moment of inertia, rotational kinetic energy and angular velocity will change but according to the law of conservation of momentum, angular momentum will not change.
In free space, neither acceleration due to gravity for external torque act on the rotating solid sphere. Therefore, taking the same mass of sphere if the radius is increased then a moment of inertia, rotational kinetic energy and angular velocity will change but according to the law of conservation of momentum, angular momentum will not change.
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A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected ?[AIEEE 2004]a)Moment of inertiab)Angular momentumc)Angular velocityd)Rotational kinetic energyCorrect answer is option 'B'. Can you explain this answer?
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A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected ?[AIEEE 2004]a)Moment of inertiab)Angular momentumc)Angular velocityd)Rotational kinetic energyCorrect 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 solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected ?[AIEEE 2004]a)Moment of inertiab)Angular momentumc)Angular velocityd)Rotational kinetic energyCorrect 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 solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected ?[AIEEE 2004]a)Moment of inertiab)Angular momentumc)Angular velocityd)Rotational kinetic energyCorrect answer is option 'B'. Can you explain this answer?.
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