Answer
$9.14cm$
Work Step by Step
We know that
$\Sigma \tau=(L-b)F-(X_{cm}-L)mg=0$
This simplifies to:
$L=\frac{X_{cm}mg+bF}{F+mg}$
We plug in the known values to obtain:
$L=\frac{\frac{1}{2}(0.122)(9.81)+(1.41)(0.365)}{(0.365)+(0.122)(9.81)}$
$L=9.14cm$
