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A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius r and outer radius R are such that r2 =R2 /2 , and the acceleration due to gravity is g. If the time period of small amplitude simple harmonic motion is given by , where pπ is the ratio of circumference to diameter of a circle, then β = ________ (round off to 2 decimal places).
    Correct answer is '2.659'. Can you explain this answer?
    Most Upvoted Answer
    A rigid uniform annular disc is pivoted on a knife edge A in a uniform...
    Given,

    Where,
    r = Inner radius of disc
    R = Outer radius of disc
    Motion of disc = Simple harmonic motion (SHM)
    Acceleration = g
    Time period of oscillation  … (i)

    Mass moment of inertia about centre of gravity ( IG)


    Disc rotated θ angle


    Where,
    TA → Torque about A
    α → Angular acceleration
     …. (iii)
    We know,
    …. (iv)
    We know,

    Since, Time period

    From equation (i) & (v)

    β = 2.659 rad/s
    Hence, the correct answer is 2.659. 
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    A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius r and outer radius R are such that r2 =R2 /2 , and the acceleration due togravity is g. If the time period of small amplitude simple harmonic motion is given by,where pπ is the ratio of circumference to diameter of a circle, then β = ________ (round off to 2 decimal places).Correct answer is '2.659'. Can you explain this answer?
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    A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius r and outer radius R are such that r2 =R2 /2 , and the acceleration due togravity is g. If the time period of small amplitude simple harmonic motion is given by,where pπ is the ratio of circumference to diameter of a circle, then β = ________ (round off to 2 decimal places).Correct answer is '2.659'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius r and outer radius R are such that r2 =R2 /2 , and the acceleration due togravity is g. If the time period of small amplitude simple harmonic motion is given by,where pπ is the ratio of circumference to diameter of a circle, then β = ________ (round off to 2 decimal places).Correct answer is '2.659'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius r and outer radius R are such that r2 =R2 /2 , and the acceleration due togravity is g. If the time period of small amplitude simple harmonic motion is given by,where pπ is the ratio of circumference to diameter of a circle, then β = ________ (round off to 2 decimal places).Correct answer is '2.659'. Can you explain this answer?.
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