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A particle performing uniform circular motion has angular momentum L, its angular frequency & halved and its rotational kinetic energy halved, then the new angular momentum is. A)4L B)2L C)L D).25L?
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A particle performing uniform circular motion has angular momentum L, ...
Explanation:
Given:
- Initial angular momentum, L
- Initial angular frequency halved, ω/2
- Initial rotational kinetic energy halved, K/2
Angular Momentum:
- The angular momentum of a particle performing uniform circular motion is given by L = Iω, where I is the moment of inertia and ω is the angular frequency.
- When the angular frequency is halved, the new angular momentum becomes L' = I(ω/2) = (1/2)Iω = (1/2)L.
- Therefore, the new angular momentum is half of the initial angular momentum, which is L/2.
Rotational Kinetic Energy:
- The rotational kinetic energy of a particle is given by K = (1/2)Iω^2.
- When the angular frequency is halved, the new rotational kinetic energy becomes K' = (1/2)I(ω/2)^2 = (1/2)I(ω^2/4) = (1/8)Iω^2 = (1/8)K.
- Therefore, the new rotational kinetic energy is one-eighth of the initial rotational kinetic energy, which is K/8.
Conclusion:
- Since angular momentum is conserved in the absence of external torques, the new angular momentum after halving the angular frequency and rotational kinetic energy is L/2.
- Therefore, the correct answer is C) L/2.
Given:
- Initial angular momentum, L
- Initial angular frequency halved, ω/2
- Initial rotational kinetic energy halved, K/2
Angular Momentum:
- The angular momentum of a particle performing uniform circular motion is given by L = Iω, where I is the moment of inertia and ω is the angular frequency.
- When the angular frequency is halved, the new angular momentum becomes L' = I(ω/2) = (1/2)Iω = (1/2)L.
- Therefore, the new angular momentum is half of the initial angular momentum, which is L/2.
Rotational Kinetic Energy:
- The rotational kinetic energy of a particle is given by K = (1/2)Iω^2.
- When the angular frequency is halved, the new rotational kinetic energy becomes K' = (1/2)I(ω/2)^2 = (1/2)I(ω^2/4) = (1/8)Iω^2 = (1/8)K.
- Therefore, the new rotational kinetic energy is one-eighth of the initial rotational kinetic energy, which is K/8.
Conclusion:
- Since angular momentum is conserved in the absence of external torques, the new angular momentum after halving the angular frequency and rotational kinetic energy is L/2.
- Therefore, the correct answer is C) L/2.
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A particle performing uniform circular motion has angular momentum L, its angular frequency & halved and its rotational kinetic energy halved, then the new angular momentum is. A)4L B)2L C)L D).25L?
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A particle performing uniform circular motion has angular momentum L, its angular frequency & halved and its rotational kinetic energy halved, then the new angular momentum is. A)4L B)2L C)L D).25L? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle performing uniform circular motion has angular momentum L, its angular frequency & halved and its rotational kinetic energy halved, then the new angular momentum is. A)4L B)2L C)L D).25L? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle performing uniform circular motion has angular momentum L, its angular frequency & halved and its rotational kinetic energy halved, then the new angular momentum is. A)4L B)2L C)L D).25L?.
A particle performing uniform circular motion has angular momentum L, its angular frequency & halved and its rotational kinetic energy halved, then the new angular momentum is. A)4L B)2L C)L D).25L? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle performing uniform circular motion has angular momentum L, its angular frequency & halved and its rotational kinetic energy halved, then the new angular momentum is. A)4L B)2L C)L D).25L? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle performing uniform circular motion has angular momentum L, its angular frequency & halved and its rotational kinetic energy halved, then the new angular momentum is. A)4L B)2L C)L D).25L?.
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