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A plate of mass m and radius r slips on a rough horizontal plane. At some instant it has translation velocity V and rotational velocity V/3r. The translation velocity after the plate start pure rolling is
- a)6V/7
- b)7V/9
- c)2V/5
- d)2V/3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A plate of mass m and radius r slips on a rough horizontal plane. At ...
Velocity of centre of rolling = V m/s
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Angular Velocity of rolling (ω) = V/3r m/s
i.e., initially, V > r ω
So, the plate will slip forward and thus the friction will act backwards as shown in fig. The normal force and weight balances to each other and friction pass through point A i.e., the net external torque is zero, thus angular momentum of the system will be conserved.
Initial angular momentum = Jcm + mrV = Icm ω + mrV
= mr2/2 ×V/3r + mrV =7/6 mrV
The final angular moment about A = mr2/2 × V2/r + mrV2 = 3/2mrV2
Using conservation of principle of angular momentum
7/6mrV = 3/2mrV2
V2 = 7V/9
Most Upvoted Answer
A plate of mass m and radius r slips on a rough horizontal plane. At ...
Velocity of centre of rolling = V m/s
Angular Velocity of rolling (ω) = V/3r m/s
i.e., initially, V > r ω
So, the plate will slip forward and thus the friction will act backwards as shown in fig. The normal force and weight balances to each other and friction pass through point A i.e., the net external torque is zero, thus angular momentum of the system will be conserved.
Initial angular momentum = Jcm + mrV = Icm ω + mrV
= mr2/2 ×V/3r + mrV =7/6 mrV
The final angular moment about A = mr2/2 × V2/r + mrV2 = 3/2mrV2
Using conservation of principle of angular momentum
7/6mrV = 3/2mrV2
V2 = 7V/9
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A plate of mass m and radius r slips on a rough horizontal plane. At some instant it has translation velocity V and rotational velocity V/3r. The translation velocity after the plate start pure rolling isa)6V/7b)7V/9c)2V/5d)2V/3Correct answer is option 'B'. Can you explain this answer?
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A plate of mass m and radius r slips on a rough horizontal plane. At some instant it has translation velocity V and rotational velocity V/3r. The translation velocity after the plate start pure rolling isa)6V/7b)7V/9c)2V/5d)2V/3Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A plate of mass m and radius r slips on a rough horizontal plane. At some instant it has translation velocity V and rotational velocity V/3r. The translation velocity after the plate start pure rolling isa)6V/7b)7V/9c)2V/5d)2V/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plate of mass m and radius r slips on a rough horizontal plane. At some instant it has translation velocity V and rotational velocity V/3r. The translation velocity after the plate start pure rolling isa)6V/7b)7V/9c)2V/5d)2V/3Correct answer is option 'B'. Can you explain this answer?.
A plate of mass m and radius r slips on a rough horizontal plane. At some instant it has translation velocity V and rotational velocity V/3r. The translation velocity after the plate start pure rolling isa)6V/7b)7V/9c)2V/5d)2V/3Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A plate of mass m and radius r slips on a rough horizontal plane. At some instant it has translation velocity V and rotational velocity V/3r. The translation velocity after the plate start pure rolling isa)6V/7b)7V/9c)2V/5d)2V/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plate of mass m and radius r slips on a rough horizontal plane. At some instant it has translation velocity V and rotational velocity V/3r. The translation velocity after the plate start pure rolling isa)6V/7b)7V/9c)2V/5d)2V/3Correct answer is option 'B'. Can you explain this answer?.
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