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A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.
[AIEEE 2011]
- a)Continuously decreases
- b)Remains unchanged
- c)First increases and then decreases
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A thin horizontal circular disc is rotating about a vertical axis pass...
Angular momentum L=Iω
L=mr2×ω
Since r first decreases then increases.
So due to conservation of angular momentum L first increases then decreases.
L=mr2×ω
Since r first decreases then increases.
So due to conservation of angular momentum L first increases then decreases.
Most Upvoted Answer
A thin horizontal circular disc is rotating about a vertical axis pass...
Explanation:
When the insect moves along the diameter of the disc, it causes a shift in the distribution of mass of the disc. This shift in the distribution of mass causes a change in the moment of inertia of the disc.
Initially, the moment of inertia of the disc is given by:
I = (1/2)MR^2
Where M is the mass of the disc and R is the radius of the disc.
When the insect moves along the diameter of the disc, the moment of inertia of the disc changes. Let the new moment of inertia of the disc be I'. The new moment of inertia of the disc can be given by:
I' = (1/4)MR^2 + 2m(d/2)^2
Where m is the mass of the insect and d is the distance of the insect from the centre of the disc.
As the insect moves towards the centre of the disc, d decreases, and hence, the moment of inertia of the disc increases. Therefore, the angular speed of the disc decreases to conserve angular momentum.
As the insect moves towards the other end of the diameter, d increases, and hence, the moment of inertia of the disc decreases. Therefore, the angular speed of the disc increases to conserve angular momentum.
Hence, the angular speed of the disc first increases and then decreases when the insect moves along a diameter of the disc to reach its other end.
When the insect moves along the diameter of the disc, it causes a shift in the distribution of mass of the disc. This shift in the distribution of mass causes a change in the moment of inertia of the disc.
Initially, the moment of inertia of the disc is given by:
I = (1/2)MR^2
Where M is the mass of the disc and R is the radius of the disc.
When the insect moves along the diameter of the disc, the moment of inertia of the disc changes. Let the new moment of inertia of the disc be I'. The new moment of inertia of the disc can be given by:
I' = (1/4)MR^2 + 2m(d/2)^2
Where m is the mass of the insect and d is the distance of the insect from the centre of the disc.
As the insect moves towards the centre of the disc, d decreases, and hence, the moment of inertia of the disc increases. Therefore, the angular speed of the disc decreases to conserve angular momentum.
As the insect moves towards the other end of the diameter, d increases, and hence, the moment of inertia of the disc decreases. Therefore, the angular speed of the disc increases to conserve angular momentum.
Hence, the angular speed of the disc first increases and then decreases when the insect moves along a diameter of the disc to reach its other end.
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Community Answer
A thin horizontal circular disc is rotating about a vertical axis pass...
Our system is :--> Disc + Insect
As external torque is zero , which means (tau = 0)
So , angular moment is conserved
From, conservation of angular momentum
I1W1 = I2W2
When insect is moving from edge to centre , then r will be decrease and w(angular velocity) will be increse.
When insect is moving from centre to edge , then r will be increase and w(angular velocity) will be decrease.
So, here correct answer is option (C) that is "First increase and then decreases"...
$$Hope it's help... $$
As external torque is zero , which means (tau = 0)
So , angular moment is conserved
From, conservation of angular momentum
I1W1 = I2W2
When insect is moving from edge to centre , then r will be decrease and w(angular velocity) will be increse.
When insect is moving from centre to edge , then r will be increase and w(angular velocity) will be decrease.
So, here correct answer is option (C) that is "First increase and then decreases"...
$$Hope it's help... $$
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A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.[AIEEE 2011]a)Continuously decreasesb)Remains unchangedc)First increases and then decreasesd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.[AIEEE 2011]a)Continuously decreasesb)Remains unchangedc)First increases and then decreasesd)None of theseCorrect answer is option 'C'. 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 thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.[AIEEE 2011]a)Continuously decreasesb)Remains unchangedc)First increases and then decreasesd)None of theseCorrect answer is option 'C'. 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 thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.[AIEEE 2011]a)Continuously decreasesb)Remains unchangedc)First increases and then decreasesd)None of theseCorrect answer is option 'C'. Can you explain this answer?.
A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.[AIEEE 2011]a)Continuously decreasesb)Remains unchangedc)First increases and then decreasesd)None of theseCorrect answer is option 'C'. 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 thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.[AIEEE 2011]a)Continuously decreasesb)Remains unchangedc)First increases and then decreasesd)None of theseCorrect answer is option 'C'. 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 thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.[AIEEE 2011]a)Continuously decreasesb)Remains unchangedc)First increases and then decreasesd)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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