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 path which lies in a horizantal plane. The length of the string 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)`

Options

A. `(3)/(2 pi) sqrt((Mg)/(mL))`
B. `2 pi sqrt((mL)/(Mg))`
C. `(1)/(2 pi) sqrt((Mg)/(mL))`
D. `(1)/(2 pi) sqrt((L)/(g))`

Answer

C

Explanation

T = mb (1) For hanging mass
`T sin theta = m (L sin theta) omega^(2)` (2) for m
From (1) and (2)
`omega^(2) = (mg)/(mL) f = (1)/(2 pi) sqrt((Mg)/(mL))`