A large mass `M` and a small mass `m` hang at the two ends of string that passes through a smooth tube as shown in fig. The mass `m` moves around in a circular peth which lies in a horizantal plane. The length of the stribng from the mass `m` to the top of the tube is of length `l` and `theta` is the angle this length makes with the vertical, what should be the frequency of rotation of the mass `m` so that `M` remains stationary if `M=16kg, m=4kg, l=1m` and `g=pi^(2)m//s^(2)`

Answer

A

Explanation

The mass `m` is acted by two forces
i) weight `mg` a mass `M` ii) Tension `T` is the string
`T cos theta=mg , T sin theta=mromega^(2)` and `T=Mg`
`r=l sin theta, Mg sin theta=m(l sin theta) omega^(2)`
`omega^(2)=(Mg)/(ml) , n=1/(2pi) sqrt((Mg)/(ml))`