An inclined plane of angule a is fixed onto a horizontal turntable with its line of greater slope in same plane as a diameter of forntable .A small block is placed on the inclined plane a distance `r` from the axis the coefficient of fraction between the block and the inclined plane is `mu` The turntable along with incline plane spins about its axis with constant minimum angular velocity `omega`

a. Find an capression for the minimum angular velocity `omega` to prevent the block from sliding down the plane in term of `g, r, mu ` and the plane `omega`
b. Now a block of mass but having coefficient friction (with inclined plane)`2mu` is kept instead of the original block . find the radius of friction force acting between block and incline now to the friction force active in part (a)

Explanation

Net force along verticle axis is zero and along redial provides centripertal acceleration

` mu N sin alpha + N cos alpha - mg = 0`
`N sin alpha - mu N cos alpha = m omega^(2) r`
`mg. ((sin alpha - mu N cos alpha))/((mu sin alpha + cos alpha))`
As block remain at same height and radial distance requirement of friction is same as in part (b)

Force of friction will remain unchanged Hence ratio as `L`