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A solid sphere is rotating freely about its symmetryaxis in free space. The radius of the sphere isincreased keeping its mass same. Which of thefollowing physical quantities would remain constantfor the sphere ?
- a)Angular velocity
- b)Moment of inertia
- c)Rotational kinetic energy
- d)Angular momentum
Correct answer is option 'D'. Can you explain this answer?
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A solid sphere is rotating freely about its symmetryaxis in free space...
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A solid sphere is rotating freely about its symmetryaxis in free space...
Angular momentum is conserved for a rotating object
- Angular momentum is a fundamental property of a rotating object and is defined as the product of the moment of inertia and the angular velocity.
- The moment of inertia depends on the distribution of mass in the object and the axis of rotation.
- When the radius of the sphere is increased while keeping its mass the same, the moment of inertia changes.
- The moment of inertia of a solid sphere is given by the equation I = (2/5) * m * r^2, where m is the mass of the sphere and r is the radius.
- As the radius is increased, the moment of inertia also increases. This means that the distribution of mass in the sphere has changed, resulting in a different moment of inertia.
- However, the mass of the sphere remains the same, so its angular momentum must remain constant.
Explanation of the other options:
a) Angular velocity: The angular velocity of the sphere is not constant because the radius is changed. The angular velocity is given by the equation ω = v/r, where v is the linear velocity and r is the radius. Since the radius is increased, the angular velocity will decrease to maintain the same linear velocity.
b) Moment of inertia: The moment of inertia changes when the radius of the sphere is increased. The moment of inertia is a measure of an object's resistance to changes in its rotational motion. When the mass is kept the same but the radius is increased, the distribution of mass changes, resulting in a different moment of inertia.
c) Rotational kinetic energy: The rotational kinetic energy of a rotating object is given by the equation KE = (1/2) * I * ω^2, where I is the moment of inertia and ω is the angular velocity. Since the moment of inertia changes when the radius is increased, the rotational kinetic energy will also change.
d) Angular momentum: As mentioned earlier, the angular momentum of the sphere remains constant because the mass is kept the same. The angular momentum is given by the equation L = I * ω, where I is the moment of inertia and ω is the angular velocity. Since the mass is the same, the moment of inertia changes to compensate for the change in the radius, resulting in a constant angular momentum.
- Angular momentum is a fundamental property of a rotating object and is defined as the product of the moment of inertia and the angular velocity.
- The moment of inertia depends on the distribution of mass in the object and the axis of rotation.
- When the radius of the sphere is increased while keeping its mass the same, the moment of inertia changes.
- The moment of inertia of a solid sphere is given by the equation I = (2/5) * m * r^2, where m is the mass of the sphere and r is the radius.
- As the radius is increased, the moment of inertia also increases. This means that the distribution of mass in the sphere has changed, resulting in a different moment of inertia.
- However, the mass of the sphere remains the same, so its angular momentum must remain constant.
Explanation of the other options:
a) Angular velocity: The angular velocity of the sphere is not constant because the radius is changed. The angular velocity is given by the equation ω = v/r, where v is the linear velocity and r is the radius. Since the radius is increased, the angular velocity will decrease to maintain the same linear velocity.
b) Moment of inertia: The moment of inertia changes when the radius of the sphere is increased. The moment of inertia is a measure of an object's resistance to changes in its rotational motion. When the mass is kept the same but the radius is increased, the distribution of mass changes, resulting in a different moment of inertia.
c) Rotational kinetic energy: The rotational kinetic energy of a rotating object is given by the equation KE = (1/2) * I * ω^2, where I is the moment of inertia and ω is the angular velocity. Since the moment of inertia changes when the radius is increased, the rotational kinetic energy will also change.
d) Angular momentum: As mentioned earlier, the angular momentum of the sphere remains constant because the mass is kept the same. The angular momentum is given by the equation L = I * ω, where I is the moment of inertia and ω is the angular velocity. Since the mass is the same, the moment of inertia changes to compensate for the change in the radius, resulting in a constant angular momentum.
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A solid sphere is rotating freely about its symmetryaxis in free space...
L=iw so L doesn't depend on mass
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A solid sphere is rotating freely about its symmetryaxis in free space. The radius of the sphere isincreased keeping its mass same. Which of thefollowing physical quantities would remain constantfor the sphere ?a)Angular velocityb)Moment of inertiac)Rotational kinetic energyd)Angular momentumCorrect answer is option 'D'. Can you explain this answer?
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A solid sphere is rotating freely about its symmetryaxis in free space. The radius of the sphere isincreased keeping its mass same. Which of thefollowing physical quantities would remain constantfor the sphere ?a)Angular velocityb)Moment of inertiac)Rotational kinetic energyd)Angular momentumCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid sphere is rotating freely about its symmetryaxis in free space. The radius of the sphere isincreased keeping its mass same. Which of thefollowing physical quantities would remain constantfor the sphere ?a)Angular velocityb)Moment of inertiac)Rotational kinetic energyd)Angular momentumCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere is rotating freely about its symmetryaxis in free space. The radius of the sphere isincreased keeping its mass same. Which of thefollowing physical quantities would remain constantfor the sphere ?a)Angular velocityb)Moment of inertiac)Rotational kinetic energyd)Angular momentumCorrect answer is option 'D'. Can you explain this answer?.
A solid sphere is rotating freely about its symmetryaxis in free space. The radius of the sphere isincreased keeping its mass same. Which of thefollowing physical quantities would remain constantfor the sphere ?a)Angular velocityb)Moment of inertiac)Rotational kinetic energyd)Angular momentumCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid sphere is rotating freely about its symmetryaxis in free space. The radius of the sphere isincreased keeping its mass same. Which of thefollowing physical quantities would remain constantfor the sphere ?a)Angular velocityb)Moment of inertiac)Rotational kinetic energyd)Angular momentumCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere is rotating freely about its symmetryaxis in free space. The radius of the sphere isincreased keeping its mass same. Which of thefollowing physical quantities would remain constantfor the sphere ?a)Angular velocityb)Moment of inertiac)Rotational kinetic energyd)Angular momentumCorrect answer is option 'D'. Can you explain this answer?.
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