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A straight rigid rod of mass M and lengt...

A straight rigid rod of mass `M` and length `L` lies on a smooth horizontal table. Taking the co-ordinate axes as shown in the figure and assuming an average force `ltFgt` acting for a small time interval `(/_\t)`, at the end `A`, making an angle `30^@` with the `X`-axis, Based on the above passege, answer the following questions.
Angular velocity of rod about `O` is

A

`(3sqrt(5)ltFgt(/_\t))/(ML)`

B

`(2sqrt(5)ltFgt(/_\t))/(ML)`

C

`(2sqrt(3)ltFgt(/_\t))/(ML)`

D

`(3sqrt(3)ltFgt(/_\t))/(ML)`

Text Solution

Verified by Experts

The correct Answer is:
D
Angular impulse `=/_\Iomega`
`sqrt3/4(:F:)/_\xxL=(ML^2)/12xximpliesomega=(3sqrt3( : F : )/_\L)/(ML)`
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