A large mass M and a small mass m hang at two ends of a string that passes over a smooth tube as shown in the figure. The mass m moves around a circular path which lies in a horizontal plane. The length of string from the mass m to the top of the tube is l and `theta` is the 'angle' this length makes with the vertical. What should be the frequency of rotation of mass m, so that the mass M remains stationary?

Explanation

For `M:T=Mg`
For `m:T sin theta=momega^(2)r`
`Mg sin theta=m omega^(2)Lsin theta`
`omega^(2)=(Mg)/(mL)`
`omega=sqrt((Mg)/(mL))`
`2pif=sqrt((Mg)/(mL))`
`f=(1)/(2pi)sqrt((Mg)/(mL))`
where `f` is the frequency of rotation of `m`.