The figure from below shows a homogeneous bar with the shape of an $L$ which mass is $6\,kg$ and its length is $30\,cm$. Find the mass of the block which is hanging from a wire and pulley tied to the end of the bar such that it is in equilibrium in the position shown. You may use the gravity $g=10\frac{m}{s^2}$.

The alternatives given are as follows:

$\begin{array}{ll}

1.&4\,kg\\

2.&10\,kg\\

3.&15\,kg\\

4.&20\,kg\\

5.&24\,kg\\

\end{array}$

I'm not sure how to make the right interpretation of the torque in this problem. How should I make the vector decomposition?. The figure from below shows how I attempted to use those vectors.

However I don't know where should I put the center of mass in this weird object. Is it in the middle?. Is it at $15\,cm$ going from the wall where the joint is put?.

From the drawing I could spot that the torque for the system would be as follows:

I'm assuming that the force on $x-axis$ will not generate torque.

$-60(15)+10m(\sin 37^{\circ})(20)=0$

$120m=900$

$m=7.5\,kg$

Although I arrived to an answer it does not check with any of the alternatives. Can someone help me to find where exactly did I made the mistake?. Can someone help me with a solution using trigonometry approach and vector decomposition?. I would like that an answer could include a method also to calculate or find the center of mass in such a figure. Will this be relevant for the solution of this problem?.