If a ring of mass m is threaded on a string of length
tied to points A and B with B vertically below A and l >AB the ring can be made to execute circular horizontal motion.
Resolving vertically for the ring gives
(1)
Using
horizontally gives
(2)
gives
Hence
(3)
Simple trigonometry gives
and
and since the length of the string is
Substitute this into (3) to obtain