JEE Main 2022 — Rotational Motion Question with Solution

A pulley of radius $$1.5\mathrm{m}$$ is rotated about its axis by a force $$F=\left(12\mathrm{t}-3{\mathrm{t}}^2\right)N$$ applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is $$4.5\mathrm{kg}{\mathrm{m}}^2$$, the number of rotations made by the pulley before its direction of motion is reversed, will be $$\frac{K}{\pi }$$. The value of K is ___________.