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Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut?
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Two small discs. A of mass 2m and B of mass m, are connected by a ligh...
Problem Overview
Two discs, A (mass 2m) and B (mass m), are connected by a string of length 13l on a smooth horizontal plane. They are initially separated by a distance of 5l. When disc B is given a velocity of 26v perpendicular to the line connecting A and B, we need to find the velocity of A when the string becomes taut.
Initial Conditions
- Mass of Disc A: 2m
- Mass of Disc B: m
- Initial distance between A and B: 5l
- Length of the string: 13l
- Velocity of Disc B: 26v (normal to AB)
Key Concepts
- The string will become taut when the total distance between the two discs equals the length of the string.
- Initially, the distance between A and B is 5l; thus, the remaining length of the string when taut is 13l - 5l = 8l.
Relative Motion
- As disc B moves perpendicularly, it creates a right triangle with the distance traveled by B and the remaining distance to A.
- Let the distance moved by B when the string becomes taut be 'd'. According to the Pythagorean theorem:
(5l + d)^2 = (8l)^2
Calculate d
- Solving gives d = 3√(13)l.
- The time taken for this motion is t = d / (26v).
Momentum Conservation
- The system's center of mass remains stationary. Thus, the momentum before and after must be conserved.
- Before the tautness, the momentum is only from disc B. The momentum of A when the string is taut (momentum_A) must equal the momentum of B:
2m * v_A = m * (26v)
Final Velocity of A
- From the conservation of momentum, we can solve for v_A:
v_A = (26v) / 2 = 13v.
Conclusion
When the string becomes taut, the velocity of disc A is 13v.
Two discs, A (mass 2m) and B (mass m), are connected by a string of length 13l on a smooth horizontal plane. They are initially separated by a distance of 5l. When disc B is given a velocity of 26v perpendicular to the line connecting A and B, we need to find the velocity of A when the string becomes taut.
Initial Conditions
- Mass of Disc A: 2m
- Mass of Disc B: m
- Initial distance between A and B: 5l
- Length of the string: 13l
- Velocity of Disc B: 26v (normal to AB)
Key Concepts
- The string will become taut when the total distance between the two discs equals the length of the string.
- Initially, the distance between A and B is 5l; thus, the remaining length of the string when taut is 13l - 5l = 8l.
Relative Motion
- As disc B moves perpendicularly, it creates a right triangle with the distance traveled by B and the remaining distance to A.
- Let the distance moved by B when the string becomes taut be 'd'. According to the Pythagorean theorem:
(5l + d)^2 = (8l)^2
Calculate d
- Solving gives d = 3√(13)l.
- The time taken for this motion is t = d / (26v).
Momentum Conservation
- The system's center of mass remains stationary. Thus, the momentum before and after must be conserved.
- Before the tautness, the momentum is only from disc B. The momentum of A when the string is taut (momentum_A) must equal the momentum of B:
2m * v_A = m * (26v)
Final Velocity of A
- From the conservation of momentum, we can solve for v_A:
v_A = (26v) / 2 = 13v.
Conclusion
When the string becomes taut, the velocity of disc A is 13v.
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Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut?
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Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut?.
Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut?.
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Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut?, a detailed solution for Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut? has been provided alongside types of Two small discs. A of mass 2m and B of mass m, are connected by a light, inextensible string of length 13l, placed on a smooth horizontal plane, separated by a distance of 5l . Disc B is given a velocity 26v in a direction normal to AB as shown fig. Find the velocity of A when the string just becomes taut? theory, EduRev gives you an
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