IRODOV PROBLEM... PLS HELP

as we know that

torque = - Icm alpha(as it is decelerating)

Icm = MR²/2(as it is a disc)

and torque = k√w
and alpha=dw/dt

hence we get

∫dw/√w=∫2k/MR²dt

first inetgrate it left = w0 to w(at any point of time)
and the right from 0 to t

u will get w as a function of T = (i)

what you have to find is
mean value of w

=₀∫^Twdt/T

T = time required to stop (which you can get by putting w=0 in (i) and calculating T)

and as you already have w as a function of t

you can do the above integration
the answer will come out to be =w₀/3