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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 abota smooth horizontal axis hinged at point `H`. Find the force exerted by the hinge just after rod is released from rest, from initial horizontal position?

Text Solution

Verified by Experts

Free body diagram of the rod

In the previous problem
`a=(3g)/(2l)`
Hence `a_(CM)=a_(t)=(alphal)/2=(3g)/4`
From the free body diagram in the vertical direction
`mg-N_(1)=ma_(CM)=m((3g)/4)`
`implies N_(1)=(mg)/4`
In horizontal direction
`F_(ext)=ma(CM)impliesN_(2)=0`
(`:'a_(CM)` in horizontal `=0` as `omega=0` just after release)
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Knowledge Check

  • A rod of mass m and length l is hinged at 'its' end and released from rest in position shown. Find the force exerted by the hinge when the rod becomes horizontal

    A
    `(mg)/4`
    B
    `(3mg)/2 cos theta`
    C
    `(mg)/4sqrt(9cos^(2)theta+1/4)`
    D
    `(mg)/2 sqrt(9 cos^(2)theta+1/4)`

  • A disc of mass M and radius R can rotate freely in a vertical plane about a horizontal axis at O distance r from the centre of the disc as shown in Fig. The disc is released from rest in the shown position. Answer the following questions based on the above information Reaction force exerted by the hinge on the disc at this instant is

    A
    `(Mg)/(5(R^(2)+2r^(2)))xxsqrt(9(R^(2)+6r^(2))^(2)+(4R^(2))^(2))`
    B
    `(Mg)/(5(R^(2)+2r^(2)))xx3(R^(2)+6r^(2))`
    C
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    D
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  • A uniform rod of mass m and length l is fixed from Point A , which is at a distance l//4 from one end as shown in the figure. The rod is free to rotate in a vertical plane. The rod is released from the horizontal position. What is the reaction at the hinge, when kinetic energy of the rod is maximum?

    A
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    C
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