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A uniform circular disc has radius R and...


A uniform circular disc has radius `R` and mass `m`. A particle, also of mass `m`, if fixed at a point A on the edge of the disc as shown in the figure. The disc can rotate freely about a horizontal chord PQ that is at a distance `R//4` from the centre `C` of the disc. The line AC is perpendicular to `PQ`. Initially the disc is held vertical with the point A at its highest position. it is then allowed to fall, so that it starts rotation about PQ. Find the linear speed of the particle as it reaches its lowest position.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt( 5 g R )`
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Knowledge Check

  • The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is

    A
    `MR^(2)`
    B
    `1/2MR^(2)`
    C
    `3/2MR^(2)`
    D
    `7/2MR^(2)`

  • The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is.

    A
    `(1)/(2) MR^2`
    B
    `MR^2`
    C
    `(7)/(2)MR^2`
    D
    `(3)/(2) MR^2`

  • A quarter disc of radius R and mass m is rotating about the axis OO' (perpendicular to the plane of the disc) as shown. Rotational kinetic energy of the quarter disc is

    A
    `(1)/(2)mR^(2)omega^(2)`
    B
    `(1)/(4)mR^(2)omega^(2)`
    C
    `(1)/(8)mR^(2)omega^(2)`
    D
    `(1)/(16)mR^(2)omega^(2)`

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