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?

Answer

1

Explanation

The mass m is acted by two forces
(i) Weight mg a mass M (ii) Tension T in the string
`T cos theta = mg , T sin theta = m r omega^(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))`