If angular velocity of a disc depends an angle rotated `theta` as `omega=theta^(2)+2theta`, then its angular acceleration `alpha` at `theta=2` rad is :

Answer

C

Explanation

Given `r=20/pi m`
Angular velocity after second revolution
`omega=v/r=(50pi)/20=(5pi)/2`
`omega_("final")^(2)=omega_("initial")^(2)+2alpha theta`
`25/4 pi^(2)=2alpha(4pi) rArr alpha=(25 pi)/32`
`a_(t)=alphar=(25pi)/32xx20/pi=15.6`