A rod `OA` rotates about a horizontal axis through `O` with a constant aniclockwise velocity `omega = 3 red s^(-1)`. As it passes the position `theta = 0`, a small block of mass `m` is placed on it at a radial distance `r = 450 mm` if the block is observed to slip at `theta = 50^(@)` . Find the coefficient of static friction between the block and the rot

(Given that `sin 50^(@) = 0.766, cos 50^(@) = 0.64)`

Explanation

At the time of slipping maximum friction acts on the body in the frame of rod
`mg sin theta = mu N + mr omega^(2)`
Also `N = mg cos theta `
`mg sin theta = mu mg cos theta + mr omega^(2)`
Here `r = 0.45 m, theta = 50^(@)`
`sin 50^(@) = 0.766` and `cos 50^(@) = 0.64`
`mu = (mg sin theta - m r omega^(2))/(mg cos theta)= (g sin theta - r omega^(2))/(g cos theta) = 0.56`