Answer:
ω' = 2.5 rad/s
Explanation:
mass of cockroach, m = 4 kg
mass of disk, M = 6 kg
Radius of disc= R
initial angular velocity, ω = 2 rad/s
Let the final angular velocity is ω'
As no external torque is applied, so the angular momentum is constant.
Angular momentum = Moment of inertia x angular velocity
I ω = I' ω'


ω' = 2.5 rad/s
This means acceleration a is constant.
Let
a) vo be the initial speed, at t=0
b) v be the final speed after time t
c) d distance travelled in time t
Then we have:
a) v=vo+a×t
b) v²=vo²+2×a×d (Galilei's equation)
c) d=vo×t+a×t²/2
d) average speed vm=(vo+v)/2