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One end of a straight uniform 1m long ba...

One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from the rest when it makes an angle `30^(@)` from the horizontal (see figure). Its angular speed when it hits the table is given as `sqrt(n)s^(-1)`, where n is an integer. The value of n is ..............

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The correct Answer is:
15
Loss of gravitational potential energy `=` Gain in kinetic energy
`:.mg 1/2 sin 30^(@)=1/2 I omega^(2)" " :.mg1/2 (1/2) = 1/2 ((ml^(2))/(3))omega^(2)`
`rArr (mgl)/(4) = (ml^(2))/(6) omega^(2) rArr omega = sqrt((6g)/(4l))`
Velocity of end point `= omega l = sqrt((6gl)/(4))=sqrt((60)/(4))=sqrt(15)m//s :. n=15`
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