Class 12 Exam > Class 12 Questions > A non-conducting ring of mass m and radius r ...
Start Learning for Free
A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.?
Most Upvoted Answer
A non-conducting ring of mass m and radius r is lying at rest in the v...
Problem Statement
A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.
Solution
The electric field E will exert a torque on the ring causing it to oscillate about the vertical diameter. The period of oscillation can be found using the equation:
T = 2π * √(I/τ)
Step 1: Find the moment of inertia
The moment of inertia of the ring about the vertical diameter can be found using the formula:
I = (1/2) * m * r^2
Step 2: Find the torque exerted by the electric field
The torque exerted by the electric field can be found using the formula:
τ = qEr * sin(θ)
where q is the charge on the ring, E is the electric field, r is the radius of the ring, θ is the angle between the electric field and the vertical diameter, and r is the radius of the ring.
Since the ring is released from rest, the initial angle θ is 0. The torque exerted by the electric field will be maximum when the ring is at its maximum displacement from the equilibrium position, which occurs when θ = π/2.
Substituting the values in the formula:
τ = qEr
Step 3: Find the period of oscillation
Substituting the values of I and τ in the formula for the period of oscillation:
T = 2π * √(I/τ) = 2π * √((m * r^2)/(qEr))
Therefore, the period of oscillation of the ring is given by:
T = 2π * √((m * r^2)/(qEr))
Community Answer
A non-conducting ring of mass m and radius r is lying at rest in the v...
HEY Aayan
|
Explore Courses for Class 12 exam
|
|
A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.?
Question Description
A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.?.
A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.?.
Solutions for A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.? in English & in Hindi are available as part of our courses for Class 12.
Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
Here you can find the meaning of A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.? defined & explained in the simplest way possible. Besides giving the explanation of
A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.?, a detailed solution for A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.? has been provided alongside types of A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.? theory, EduRev gives you an
ample number of questions to practice A non-conducting ring of mass m and radius r is lying at rest in the vertical XY plane on a smooth non conducting horizontal XZ plane. Charge +q and –q are distributed uniformly on the ring. On the two sides of the vertical diameter of the ring. A constant and uniform electric field E is set up along the x-direction. The ring is given a small rotation about the vertical diameter of the ring and released. Find the period of oscillation of the ring.? tests, examples and also practice Class 12 tests.
|
|
Explore Courses for Class 12 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup