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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.
When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is
[JEE' 2007]
- a)2Iw/(3t)
- b)9Iw/(2t)
- c)9Iw/(4t)
- d)3Iw/(2t)
Correct answer is option 'A'. Can you explain this answer?
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Two discs A and B are mounted coaxially on a vertical axle. The discs ...
Given information:
- Two discs A and B are mounted coaxially on a vertical axle.
- The moments of inertia of disc A and disc B about the common axis are I and 2I respectively.
- 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 using a spring with the same spring constant and compressed by a distance x2.
- Both discs rotate in the clockwise direction.
To find:
The average frictional torque on one disc by the other during the time period t when they acquire a common angular velocity.
Solution:
The total mechanical energy of the system is conserved when the two discs are brought in contact. Initially, disc A has an angular velocity of 2w and disc B has an angular velocity of w.
Step 1: Finding the common angular velocity.
- Since the total mechanical energy is conserved, the sum of the kinetic energies of the two discs before and after contact should be the same.
- The kinetic energy of disc A before contact is given by (1/2)*I*(2w)^2 = 2Iw^2.
- The kinetic energy of disc B before contact is given by (1/2)*(2I)*(w)^2 = 2Iw^2.
- The total kinetic energy before contact is 2Iw^2 + 2Iw^2 = 4Iw^2.
- The total kinetic energy after contact is (1/2)*I*(2w + w)^2 = (1/2)*I*(3w)^2 = 9Iw^2/2.
- Therefore, 4Iw^2 = 9Iw^2/2.
- Simplifying the equation, we get 8Iw^2 = 9Iw^2.
- Dividing by Iw^2 on both sides, we get 8 = 9.
- This implies that the common angular velocity of the two discs is 2w.
Step 2: Finding the average frictional torque.
- The average frictional torque can be calculated by considering the change in angular momentum during the time period t.
- The angular momentum of disc A before contact is given by I*(2w).
- The angular momentum of disc B before contact is given by (2I)*w = 2Iw.
- The total angular momentum before contact is I*(2w) + 2Iw = 4Iw.
- The angular momentum after contact is (I + 2I)*(2w) = 6Iw.
- The change in angular momentum is 6Iw - 4Iw = 2Iw.
- The average frictional torque is given by the change in angular momentum divided by the time period t.
- Therefore, average frictional torque = (2Iw)/t = 2Iw/(3t).
Hence, the average frictional torque on one disc by the other during the time period t is 2Iw/(3t), which corresponds to option (a).
- Two discs A and B are mounted coaxially on a vertical axle.
- The moments of inertia of disc A and disc B about the common axis are I and 2I respectively.
- 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 using a spring with the same spring constant and compressed by a distance x2.
- Both discs rotate in the clockwise direction.
To find:
The average frictional torque on one disc by the other during the time period t when they acquire a common angular velocity.
Solution:
The total mechanical energy of the system is conserved when the two discs are brought in contact. Initially, disc A has an angular velocity of 2w and disc B has an angular velocity of w.
Step 1: Finding the common angular velocity.
- Since the total mechanical energy is conserved, the sum of the kinetic energies of the two discs before and after contact should be the same.
- The kinetic energy of disc A before contact is given by (1/2)*I*(2w)^2 = 2Iw^2.
- The kinetic energy of disc B before contact is given by (1/2)*(2I)*(w)^2 = 2Iw^2.
- The total kinetic energy before contact is 2Iw^2 + 2Iw^2 = 4Iw^2.
- The total kinetic energy after contact is (1/2)*I*(2w + w)^2 = (1/2)*I*(3w)^2 = 9Iw^2/2.
- Therefore, 4Iw^2 = 9Iw^2/2.
- Simplifying the equation, we get 8Iw^2 = 9Iw^2.
- Dividing by Iw^2 on both sides, we get 8 = 9.
- This implies that the common angular velocity of the two discs is 2w.
Step 2: Finding the average frictional torque.
- The average frictional torque can be calculated by considering the change in angular momentum during the time period t.
- The angular momentum of disc A before contact is given by I*(2w).
- The angular momentum of disc B before contact is given by (2I)*w = 2Iw.
- The total angular momentum before contact is I*(2w) + 2Iw = 4Iw.
- The angular momentum after contact is (I + 2I)*(2w) = 6Iw.
- The change in angular momentum is 6Iw - 4Iw = 2Iw.
- The average frictional torque is given by the change in angular momentum divided by the time period t.
- Therefore, average frictional torque = (2Iw)/t = 2Iw/(3t).
Hence, the average frictional torque on one disc by the other during the time period t is 2Iw/(3t), which corresponds to option (a).
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Two discs A and B are mounted coaxially on a vertical axle. The discs ...
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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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. Can you explain this answer?.
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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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Here you can find the meaning 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. 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.When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is[JEE 2007]a)2Iw/(3t)b)9Iw/(2t)c)9Iw/(4t)d)3Iw/(2t)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 11 tests.
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