A solid uniform cylinder of mass m performs small oscillations in horizontal plane if slightly displaced from its mean position shown in the figure. Initially springs are in naturals and cylinder does not slip on ground during oscillations due to friction between ground and cylinder. Force constant of each spring is k. The time period of oscillation isa)b)c)d)Correct answer is option 'C'. Can you explain this answer?

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A solid uniform cylinder of mass m performs small oscillations in horizontal plane if slightly displaced from its mean position shown in the figure. Initially springs are in naturals and cylinder does not slip on ground during oscillations due to friction between ground and cylinder. Force constant of each spring is k. The time period of oscillation is

Correct answer is option 'C'. Can you explain this answer?

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A solid uniform cylinder of mass m performs small oscillations in hori...

A snapshot during oscillations of the cylinder is shown in the figure. Its displacement is x and velocity v.
Its angular velocity is ω = V/R(Due to pure rolling)

As the centre of the cylinder is at a distance x from the initial position, the spring which are connected at a
point on its rim must be compressed and stretched by a distance 2x. Thus, at this intermediate position total
energy of the oscillation system can be given as

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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. In Fluid Friction Damping the amount of damping torque

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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

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The length of a simple pendulum is about 100 cm known to an accuracy of 1 mm. Its period of oscillation is 2s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g ?

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A solid uniform cylinder of mass m performs small oscillations in horizontal plane if slightly displaced from its mean position shown in the figure. Initially springs are in naturals and cylinder does not slip on ground during oscillations due to friction between ground and cylinder. Force constant of each spring is k. The time period of oscillation isa)b)c)d)Correct answer is option 'C'. 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 A solid uniform cylinder of mass m performs small oscillations in horizontal plane if slightly displaced from its mean position shown in the figure. Initially springs are in naturals and cylinder does not slip on ground during oscillations due to friction between ground and cylinder. Force constant of each spring is k. The time period of oscillation isa)b)c)d)Correct answer is option 'C'. 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 A solid uniform cylinder of mass m performs small oscillations in horizontal plane if slightly displaced from its mean position shown in the figure. Initially springs are in naturals and cylinder does not slip on ground during oscillations due to friction between ground and cylinder. Force constant of each spring is k. The time period of oscillation isa)b)c)d)Correct answer is option 'C'. Can you explain this answer?.

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