rotational mechanics

as water falls normally the torque delivered by it to the disc= 0
hence angular momentum remains conserved

at time t water collected= μt

L=((mR²/2)+μtR²)w
dL/dt=0

hence

(1/2)mR²dw/dt+μR²w+μtR²dw/dt=0
now you can solve for the time taken

ok nishant sir i have done it is angular momentum about the rotation axis.
rohan thnx it hellped for my soln