Consider the situation as shown in the figure. A rod of length `L=2//27m` pivodated near an end which is made to rotate in a horizontal plane with a constant angular speed. A ball is suspended bu a string also of length `2//27m` from the other end of the rod. if the string makes `theta=53^(@)` with vertical, find the angular speed of rotation.

Explanation

The ball moves in horizontal circle of radius `(L+L sin theta)`
`T cos theta)mg` …..`(i)`
`T sin theta=momega^(2) r=momega^(2)(L+L sin theta)` ….`(ii)`
Dividing `(ii)` by `(i)`,we get
`tan theta=(omega^(2)L(1+sin theta))/(g)`
`omega=sqrt((g tan theta)/(L(1+sin theta)))=sqrt((g tan 53^(@))/((2)/(27)(1+sin 53^(@))))`
`=sqrt((10xx(4)/(3))/((2)/(27)(1+(4)/(5))))=sqrt((40/(3))/((2)/(27)xx(9)/(5)))=10 rad//s`