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A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B?
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A smooth rod is mounted just above a tabletop . A 10 kg collar which i...
Analysis:
To find the velocity of the collar as it passes point B, we need to apply the principles of conservation of energy and Hooke's law.

Conservation of Energy:
When the collar is released from rest at point A, it possesses potential energy due to its displacement from the equilibrium position of the spring. As the collar moves towards point B, this potential energy is converted into kinetic energy.

Hooke's Law:
According to Hooke's law, the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The equation for Hooke's law is given by F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

Calculations:
1. Calculate the potential energy of the collar at point A:
- The potential energy of the collar is given by PE = (1/2)kx^2, where k is the spring constant and x is the displacement from the equilibrium position.
- At point A, the displacement is 10 cm = 0.1 m.
- Substitute the values into the equation: PE = (1/2)(500 N/m)(0.1 m)^2 = 2.5 J.

2. Apply the principle of conservation of energy:
- At point A, the total energy of the system is equal to the potential energy of the collar.
- As the collar moves towards point B, its potential energy is converted into kinetic energy.
- At point B, all the potential energy is converted into kinetic energy.
- Therefore, the kinetic energy of the collar at point B is equal to the potential energy at point A.
- The equation for kinetic energy is KE = (1/2)mv^2, where m is the mass of the collar and v is its velocity.
- Substitute the values into the equation: 2.5 J = (1/2)(10 kg)v^2.
- Simplify the equation: v^2 = 0.5 m^2/s^2.
- Take the square root of both sides: v ≈ 0.707 m/s.

Answer:
The velocity of the collar as it passes point B is approximately 0.707 m/s.
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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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A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B?
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A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B? 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 A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B?.
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