The angular velocity of a particle is given by $\omega =1.5t-3t^2+2$, the time when its angular acceleration ceases to exist will be -

The correct option is B $0.25\text{sec}$
It is given that $\omega =1.5t-3t^2+2$,
we know that angular acceleration refers to time rate of change of angular velocity

$\alpha =\frac{d\omega }{dt}=1.5-6t$
When the angular acceleration becomes zero, $\alpha =0$
we get,
$\Rightarrow \alpha =1.5-6t=0$
$\Rightarrow t=\frac{1.5}{6}=0.25\text{sec}$
Hence correct answer is (b)