A particle of mass m is attached to a vertical rod with two inextensible strings AO and BO of equal lengths l. Distance between A and B is also l. The setup is rotated with angular speed `omega` with rod as the axis.

(a) Find the values of `omega` for which the particle remains at point B.
(b) Find the range of values of `omega` for which tension `(T_(1))` in the string AO is greater than mg but the other string remains slack
(c) Find the value of `omega` for which tension `(T_(1))` in string AO is twice the tension `(T_(2))` in string BO
(d) Assume that both strings are taut when the string AO breaks. What will be nature of path of the particle moment after AO breaks ?

Answer

(a) `omega gt sqrt((g)/(t))`
(b) `sqrt((g)/(l)) lt omega le sqrt((2g)/(l))`
(c) `sqrt((6g)/(l))`
(d) parabollic