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Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.
The loss of kinetic energy during the above process is
[JEE' 2007]
- a)Iw2/2
- b)Iw2/3
- c)Iw2/4
- d)Iw2/6
Correct answer is option 'B'. Can you explain this answer?
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Two discs A and B are mounted coaxially on a vertical axle. The discs ...
We need to calculate the loss of kinetic energy when two discs with moments of inertia III and 2I2I2I rotate together on a common axis after being imparted with different angular velocities.
Step 1: Initial Kinetic Energy of Each Disc
Disc A:
Disc A:
- Moment of inertia I
- Angular velocity 2ω
- Rotational kinetic energy:
Disc B:
- Moment of inertia 2I
- Angular velocity ω
- Rotational kinetic energy:
Total Initial Kinetic Energy:
Step 2: Final Kinetic Energy After Interaction
Step 2: Final Kinetic Energy After Interaction
When the discs come together and rotate with a common angular velocity, the angular momentum is conserved.
- Initial Angular Momentum:
- Final Angular Momentum (since the discs rotate together):
- Using the conservation of angular momentum:
- Final Kinetic Energy:
Step 3: Loss of Kinetic Energy
The loss in kinetic energy is:
Final Answer:
The loss of kinetic energy is 
which corresponds to Option B: 
which corresponds to Option B: Free Test
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Community Answer
Two discs A and B are mounted coaxially on a vertical axle. The discs ...
Loss of kinetic energy during the process can be calculated by finding the initial and final kinetic energies of the discs.
Initial Kinetic Energy:
For disc A, the initial kinetic energy is given by 1/2 * I * (2w)² = 2Iw²
For disc B, the initial kinetic energy is given by 1/2 * 2I * w² = Iw²
Final Kinetic Energy:
The final kinetic energy can be calculated by finding the sum of the kinetic energies of both discs after the process.
Let the final angular velocities of disc A and disc B be ω₁ and ω₂ respectively.
The moment of inertia of disc A is I and its final kinetic energy is given by 1/2 * I * ω₁².
The moment of inertia of disc B is 2I and its final kinetic energy is given by 1/2 * 2I * ω₂².
Since both discs rotate in the clockwise direction, the final kinetic energy of the system is given by 1/2 * I * ω₁² + 1/2 * 2I * ω₂².
Since the discs are mounted coaxially, the total angular momentum of the system is conserved. Therefore, the sum of the initial angular momenta of the discs is equal to the sum of the final angular momenta.
The initial angular momentum of disc A is given by I * (2w) and the initial angular momentum of disc B is given by 2I * w.
The final angular momentum of disc A is given by I * ω₁ and the final angular momentum of disc B is given by 2I * ω₂.
Therefore, we have I * (2w) + 2I * w = I * ω₁ + 2I * ω₂.
Simplifying the equation, we get 2w + 2w = ω₁ + 2ω₂.
This implies ω₁ = 2w - 2ω₂.
Substituting this value of ω₁ in the expression for final kinetic energy, we get:
1/2 * I * (2w - 2ω₂)² + 1/2 * 2I * ω₂².
Expanding and simplifying the expression, we get:
2Iw² - 4Iwω₂ + 2Iω₂² + 2Iω₂².
The loss of kinetic energy is given by the difference between the initial and final kinetic energies:
2Iw² + Iw² - (2Iw² - 4Iwω₂ + 2Iω₂² + 2Iω₂²).
Simplifying the expression, we get:
Iw² + 4Iwω₂ - 4Iω₂².
Since the discs have the same spring constant, the compression distances x₁ and x₂ are related by the equation:
x₁ = 2x₂.
Using this relation, we can express ω₂ in terms of ω:
ω₂ = w * x₁ / x₂ = 2w * x₁ / 2x₂ = 2w.
Substituting this value of ω₂ in the expression for loss of kinetic energy, we get:
Iw² + 4Iw(2w) -
Initial Kinetic Energy:
For disc A, the initial kinetic energy is given by 1/2 * I * (2w)² = 2Iw²
For disc B, the initial kinetic energy is given by 1/2 * 2I * w² = Iw²
Final Kinetic Energy:
The final kinetic energy can be calculated by finding the sum of the kinetic energies of both discs after the process.
Let the final angular velocities of disc A and disc B be ω₁ and ω₂ respectively.
The moment of inertia of disc A is I and its final kinetic energy is given by 1/2 * I * ω₁².
The moment of inertia of disc B is 2I and its final kinetic energy is given by 1/2 * 2I * ω₂².
Since both discs rotate in the clockwise direction, the final kinetic energy of the system is given by 1/2 * I * ω₁² + 1/2 * 2I * ω₂².
Since the discs are mounted coaxially, the total angular momentum of the system is conserved. Therefore, the sum of the initial angular momenta of the discs is equal to the sum of the final angular momenta.
The initial angular momentum of disc A is given by I * (2w) and the initial angular momentum of disc B is given by 2I * w.
The final angular momentum of disc A is given by I * ω₁ and the final angular momentum of disc B is given by 2I * ω₂.
Therefore, we have I * (2w) + 2I * w = I * ω₁ + 2I * ω₂.
Simplifying the equation, we get 2w + 2w = ω₁ + 2ω₂.
This implies ω₁ = 2w - 2ω₂.
Substituting this value of ω₁ in the expression for final kinetic energy, we get:
1/2 * I * (2w - 2ω₂)² + 1/2 * 2I * ω₂².
Expanding and simplifying the expression, we get:
2Iw² - 4Iwω₂ + 2Iω₂² + 2Iω₂².
The loss of kinetic energy is given by the difference between the initial and final kinetic energies:
2Iw² + Iw² - (2Iw² - 4Iwω₂ + 2Iω₂² + 2Iω₂²).
Simplifying the expression, we get:
Iw² + 4Iwω₂ - 4Iω₂².
Since the discs have the same spring constant, the compression distances x₁ and x₂ are related by the equation:
x₁ = 2x₂.
Using this relation, we can express ω₂ in terms of ω:
ω₂ = w * x₁ / x₂ = 2w * x₁ / 2x₂ = 2w.
Substituting this value of ω₂ in the expression for loss of kinetic energy, we get:
Iw² + 4Iw(2w) -
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Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertiaIand 2Irespectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above process is [JEE 2007]a)Iw2/2b)Iw2/3c)Iw2/4d)Iw2/6Correct answer is option 'B'. Can you explain this answer?
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Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertiaIand 2Irespectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above process is [JEE 2007]a)Iw2/2b)Iw2/3c)Iw2/4d)Iw2/6Correct answer is option 'B'. 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 Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertiaIand 2Irespectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above process is [JEE 2007]a)Iw2/2b)Iw2/3c)Iw2/4d)Iw2/6Correct answer is option 'B'. 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 Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertiaIand 2Irespectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above process is [JEE 2007]a)Iw2/2b)Iw2/3c)Iw2/4d)Iw2/6Correct answer is option 'B'. Can you explain this answer?.
Solutions for Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertiaIand 2Irespectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above process is [JEE 2007]a)Iw2/2b)Iw2/3c)Iw2/4d)Iw2/6Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertiaIand 2Irespectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above process is [JEE 2007]a)Iw2/2b)Iw2/3c)Iw2/4d)Iw2/6Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertiaIand 2Irespectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above process is [JEE 2007]a)Iw2/2b)Iw2/3c)Iw2/4d)Iw2/6Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertiaIand 2Irespectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above process is [JEE 2007]a)Iw2/2b)Iw2/3c)Iw2/4d)Iw2/6Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertiaIand 2Irespectively about the common axis. Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance x1. Disc B is imparted an angular velocity w by a spring having the same spring constant and compressed by a distance x2. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above process is [JEE 2007]a)Iw2/2b)Iw2/3c)Iw2/4d)Iw2/6Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 11 tests.
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