The torque applied on a rigid body of moment of inertia 2 kg m ^2 varies with its angular displacement . The graph of versus is a straight line starting from the origin and reaching a maximum torque of 10 N m at an angular displacement of 20 rad . If the body starts from rest, its final angular speed at = 20 rad is:

Step-by-step solution

The work done on the body is equal to the area under the torque-angular displacement graph. Since the graph is a triangle starting from the origin: Work done (W) = 1 2 base height W = 1 2 20 rad 10 N m = 100 J According to the work-energy theorem for rotational motion, the work done is equal to the change in rotational kinetic energy: W = K = 1 2 I ^2 - 0 100 = 1 2 2 ^2 ^2 = 100 = 10 rad/s Answer: 10 rad/s