### e 13 8 151

The total mass on the right side is the mass per unit length ($\lambda$)
times the length: $m_{R}=\lambda x.$ The mass on the left side is
$m_{L}=\lambda(L-x).$
$a=\frac{m_{R}-m_{L}}{m_{R}+m_{L}}g=\frac{\lambda x-\lambda(L-x)}{\lambda x+\lambda(L-x)}g=\frac{2x-L}{L}g.$
The acceleration is in the direction of the side of length x, if $x>L/2.$