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Answer

The moment of inertia of the wheel is I = 2.5 kg m^2. The torque acting on it is T= 10 N-m. Now, From the relation, α= T/I = 10/2.5 rad/s^2= 4 rad/s^2 (angular acceleration) Since angular acceleration is the rate of change of angular velocity with respect to time. so, The time required for the wheel to go from angular velocity of 40 rad/s to 60 rad/s is t= |change in angular velocity| / angular acceleration = 60-40/4 s = 5 s Time Taken=5 seconds