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`.

Options

A. `(momegaL^(2))/(3)costheta`
B. `(momegaL^(2))/(3)sintheta`
C. `(momegaL^(2))/(6)sin2theta`
D. `(momegaL^(2))/(3)sintheta`

Explanation

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)`