Answer
$m=5kg$
Work Step by Step
According to Newton's 2nd law of rotational motion, $$\tau=I\alpha$$
Here, the force $F=45N$, when applied to the disk, produces a torque with lever arm $r=0.15m$. Therefore, $\tau=45N\times0.15m=6.75N.m$
A solid cylindrical disk has $I=\frac{1}{2}mr^2$. The disk's angular acceleration $\alpha=120rad/s^2$
$$\frac{1}{2}mr^2\alpha=\tau$$ $$m=\frac{2\tau}{r^2\alpha}=5kg$$
