Answer
$2.4m$
Work Step by Step
We know that
$\rho gL^2+p_aL-p_aH=0$
This simplifies to:
$L=\frac{-p_a\pm \sqrt{p_a^2+4\rho gp_a H}}{2\rho g}$
We plug in the known values to obtain:
$L=\frac{-101300\pm\sqrt{(101300)^2+4(1000)(9.8)(101300)(3)}}{2(1000)(9.8)}$
$L=2.4m$
