A rigid body rotates about a fixed axis with variable angular velocity ( - t ) at time t, where and are constants. The angle through which it rotates before it comes to rest is

Step-by-step solution

The angular velocity is = - t . The body reaches rest when = 0 , giving - t_f = 0 and t_f = . The total rotation angle is the integral of angular velocity over time: = ₀^ / ( - t) , dt = [ t - t^2 2 ]₀^ / Evaluating at the limits: = ( - 2 ^2 ^2 ) - 0 = ^2 - ^2 2 = ^2 2 Final answer: C