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 ?

Options

A. Tension in thread BO is greater
B. Tension in thread AO is greater
C. Tension in the two threads are equal
D. Tension in AO or BO is greater according as `omega` is anticlockwise or clockwise

Answer

B

Explanation

`T_(1) sin 30^(@) = T_(2) sin 30^(@) + mg implies t_(1) = T_(2) + 2 mg`
`implies `T_(1) gt T_(2)`