The figure shows a rod which startsm rotating with angular acceleration `alpha` about vertical axis passing through one of its end (A) in horizontal plane. A bead of mass `m` just fit's the rod and is situated at a distance 'r' from end A. Friction exists between rod and the bead with coefficient `mu`. As the angular velocity of rod increases the bead starts sliding over the rod (say after time `t_(0)`)

Based on above information answer the following question :
If the bead start sliding at `t=t_(0)` then value of `t_(0)` is given by :

Options

A. `sqrt((musqrt(g^(2)+(ralpha)^(2)))/(r alpha^(2)))`
B. `sqrt((mg)/(ralpha^(2)))`
C. `sqrt((mu sqrt(g^(2)+(r alpha)^(2)))/(r alpha^(2)))-sqrt((mg)/(r alpha^(2)))`
D. None of these

Answer

a