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A uniform rod of mass m and length l can...

A uniform rod of mass `m` and length `l` can rotate in a vertical plane about a smooth horizontal axis point `H`. a. Find angular acceleration `alpha` of the rod. just after it is released from initial horizontal position from rest'? b. Calculate the acceleration (tangential and radial) , point A at this moment.

Text Solution

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a `tau_(H)=I_(H) alpha`
`mg l/2=(ml^(2))/3alphaimplies alpha=(3g)/(2l)`
b. `a_(tA)=alphal=(3g)/(2l)l`
`=a_(CA)=omega^(2)r=0xxl`
`=0(omega=0` just after release)
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Knowledge Check

  • A uniform rod of mass 20 Kg and length 1.6 m is piovted at its end and swings freely in the vertical plane. Angular acceleration of the rod just after the rod is relased from rest in the horizontal position is

    A
    `(15g)/(16)`
    B
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    C
    `(16g)/(15)`
    D
    `(g)/(15)`

  • A unifrom rod of length l and mass m is free to rotate in a vertical plane about A as shown in Fig. The rod initially in horizontal position is released. The initial angular acceleration of the rod is

    A
    `(3g)/(2l)`
    B
    `(3g)/(l)`
    C
    `(g)/(2l)`
    D
    `(2g)/(l)`

  • A uniform rod of mass m length l is attached to smooth hinge at end A and to a string at end B as shown in figure. It is at rest. The angular acceleration of the rod just after the string is cut is :

    A
    `(3g)/(2l)`
    B
    `(3g)/(4l)`
    C
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