Two bodies $A$ and $B$ rotate about an axis,such that the angle $\theta_A$ (in radians) covered by the first body is proportional to the square of time,and $\theta_B$ (in radians) covered by the second body varies linearly with time. At $t = 0$,$\theta_A = \theta_B = 0$. If $A$ completes its first revolution in $\sqrt{\pi} \ s$ and $B$ needs $4\pi \ s$ to complete half a revolution,then the ratio of their angular velocities $\omega_A : \omega_B$ at $t = 5 \ s$ is:

• A
  $4 : 1$
• B
  $20 : 1$
• C
  $80 : 1$
• D
  $20 : 4$