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A rod of mass m and length l is rotating...

A rod of mass `m` and length `l` is rotating about a fixed point in the ceiling with an angular velocity `omega` as shown in the figure. The rod maintains a constant angle `theta` with the vertical.
What will be the horizontal component of angular momentum of the rod about the point of suspension in terms of `m`, `omega`, `l` and `theta`.

A

`(momegaL^(2))/(3)costheta`

B

`(momegaL^(2))/(3)sintheta`

C

`(momegaL^(2))/(6)sin2theta`

D

`(momegaL^(2))/(3)sintheta`

Text Solution

Verified by Experts

Consider an element of the rod.
`dL=x xx m xx xsintheta=momegax^(2)sintheta`
`rArr L=intdL=(momegaL^(2))/(3)sintheta`
Its horizontal component `= L cos theta=(momegaL^(2)sin2theta)/(6)`
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