A particle of mass `m` connected with a hanging bob of mass `M` by an inextensible string is stationary relative to the rotating platform . The coefficient of static friction between the particle and platform is `mu`

Find the
a. maximum angular speed `omega_(1)`
b. maximum angular speed `omega_(2)`
`(for M gt mu m)`

Explanation

`T = Mg`

`T + mu N = m omega^(2)R`
`Mg + muMg = m omega^(2)R`
`omega_(max) =sqrt(((M + mu m) g)/(mR))`
For maximum angular velocity , the direction of friction will be toward radius direction (away from center) Hence.
`omega_(min) =sqrt(((M + mu m) g)/(mR))`