The angular velocity of a particle is given by ω= 1.5 t - 3t² + 2 , the time when its angular acceleration ceases to be zero will be

The correct option is 0.25 sec.

Step-by-step Explanation:

Angular velocity ($\omega$) is given as a function of time ($t$) by the equation:
$\omega =1.5t-3t^2+2$

Angular acceleration ($\alpha$) is defined as the first derivative of angular velocity with respect to time:
$\alpha =\frac{d\omega }{dt}$

Differentiating the given expression for $\omega$ with respect to $t$:
$\alpha =\frac{d}{dt}(1.5t-3t^2+2)$

Applying the power rule of differentiation:
$\alpha =1.5-6t$

To find the time when the angular acceleration is zero, we set $\alpha =0$:
$1.5-6t=0$

Solving for $t$:
$6t=1.5$
$t=\frac{1.5}{6}$
$t=0.25\text{sec}$

Thus, the angular acceleration becomes zero at $t=0.25\text{sec}$.