Neglecting friction what is the final angular speed of the motor – machine combination?

Question

A motor is connected to a machine through a clutch. Moment of inertia I₁ of motor  = 10 kg m²,

and that of machine I₂ = 15 kg m². The motor is started and when it runs steadily at 100  rad/s, the

dutch is suddenly engaged and the power to the motor is cut off. Neglecting friction what is the final angular speed of the motor – machine combination?

            (a) Zero           (b) $20\sqrt{10}$ rad/s      (c) 40 rad/s     (d)   100 rad/s