Answer
It is not strong enough.
Work Step by Step
First, we need to draw the force diagram of the boy+chair as one unit as a particle in a uniform circular motion, as shown below.
Now we need to find the tension force by applying Newton's second law.
$$\sum F_y=T\cos-mg=ma_y=m(0)=0$$
Thus,
$$T=\dfrac{mg}{\cos \theta}$$
where $\cos\theta=\dfrac{h}{L}$
thus,
$$T=\dfrac{mgL}{h}$$
where $h=\sqrt{L^2-r^2}$
$$T=\dfrac{mgL}{\sqrt{L^2-r^2}}\tag 1$$
$$\sum F_r=T\sin\theta=ma_r=m\dfrac{v^2}{r}$$
where $v=\omega r$, so that
$$ T\sin\theta =m\omega^2 r$$
where $\sin\theta =\dfrac{r}{L}$
$$ T\dfrac{ \color{red}{\bf\not}r}{L}=m\omega^2 \color{red}{\bf\not}r$$
$$T=m\omega^2 L$$
Plugging the known;
$$T=150\times \left(\dfrac{2\pi }{4}\right)^2 \times 9$$
$$T=\bf 3330\;\rm N$$
Therefore, the chain is unsuitable for this tension. It is not strong enough.
