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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).
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Attempt All sub parts from each question.Damping: When an analog instrument is used to measure a physical parameter, a deflecting torque is applied to the moving system which is deflected from its initial position and should move steadily to the deflected position. But due to inertia, the moving system keeps on oscillating about equilibrium. To remove the oscillation of the moving system a damping torque is required. The damping torque should be of such that the pointer quickly comes to its final steady position, without overshooting. If the instrument is underdamped, the moving system will oscillate about the final steady position with a decreasing amplitude and will take some time before it comes to rest. When the moving system moves rapidly but smoothly to its final steady position, the instrument is said to be critically damped or deadbeat. If the damping torque is more than what is required for critical damping, the instrument is said to be overdamped. In an overdamped instrument, the moving system moves slowly to its final steady position in a lethargic fashion.Methods of producing damping torque:(i) Air friction damping(ii) Fluid friction damping(iii) Eddy current dampingAir Friction Damping: A light piston is attached to the moving system. This piston moves in an air chamber closed at one end. When there is an oscillation, the piston moves in and out of the chamber. When the piston moves into the chamber, the air inside is compressed and an air pressure is built up which opposes the motion of the piston and thus the moving system faces a damping torque which ultimately reduces the oscillation. Fluid Friction Damping: In this type of damping oil is used in place of air. Viscosity of the oil being greater, the damping torque is also more. A disc is attached to the moving system which is completely dipped into the oil. When the moving system oscillates, the disc moves in oil and a frictional drag is produced. This frictional drag opposes the oscillation. Eddy Current Damping: The moving system is connected to an aluminium disc which rotates in a magnetic field. Rotation in magnetic field induces an emf in it and if the path is closed, a current (known as eddy current) flows. This current interacts with the magnetic field to produce an electromagnetic torque which opposes the motion. This torque is proportional to the oscillation of the moving system. This electromagnetic torque ultimately reduces the oscillation. Air friction damping provides a very simple and cheap method of damping. The disadvantages of fluid friction damping are that it can be used only for instruments which are in vertical position. Eddy current damping is the most efficient form of damping.Q. The most efficient form of damping is

Attempt All sub parts from each question.Damping: When an analog instrument is used to measure a physical parameter, a deflecting torque is applied to the moving system which is deflected from its initial position and should move steadily to the deflected position. But due to inertia, the moving system keeps on oscillating about equilibrium. To remove the oscillation of the moving system a damping torque is required. The damping torque should be of such that the pointer quickly comes to its final steady position, without overshooting. If the instrument is underdamped, the moving system will oscillate about the final steady position with a decreasing amplitude and will take some time before it comes to rest. When the moving system moves rapidly but smoothly to its final steady position, the instrument is said to be critically damped or deadbeat. If the damping torque is more than what is required for critical damping, the instrument is said to be overdamped. In an overdamped instrument, the moving system moves slowly to its final steady position in a lethargic fashion.Methods of producing damping torque:(i) Air friction damping(ii) Fluid friction damping(iii) Eddy current dampingAir Friction Damping: A light piston is attached to the moving system. This piston moves in an air chamber closed at one end. When there is an oscillation, the piston moves in and out of the chamber. When the piston moves into the chamber, the air inside is compressed and an air pressure is built up which opposes the motion of the piston and thus the moving system faces a damping torque which ultimately reduces the oscillation. Fluid Friction Damping: In this type of damping oil is used in place of air. Viscosity of the oil being greater, the damping torque is also more. A disc is attached to the moving system which is completely dipped into the oil. When the moving system oscillates, the disc moves in oil and a frictional drag is produced. This frictional drag opposes the oscillation. Eddy Current Damping: The moving system is connected to an aluminium disc which rotates in a magnetic field. Rotation in magnetic field induces an emf in it and if the path is closed, a current (known as eddy current) flows. This current interacts with the magnetic field to produce an electromagnetic torque which opposes the motion. This torque is proportional to the oscillation of the moving system. This electromagnetic torque ultimately reduces the oscillation. Air friction damping provides a very simple and cheap method of damping. The disadvantages of fluid friction damping are that it can be used only for instruments which are in vertical position. Eddy current damping is the most efficient form of damping.Q. In Fluid Friction Damping the amount of damping torque

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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?.
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