$\Rightarrow m a=\sigma V g-\rho V g$

$\Rightarrow(\rho V) a=V g(\sigma-\rho)$

$\Rightarrow a=g\left(\frac{\sigma}{\rho}-1\right)$

Velocity $v$ after height $h=\sqrt{2 g\left(\frac{\sigma}{\rho}-1\right) h}$

Conserving mechanical energy at max height h'above surface,

$m g h^{\prime}=\frac{1}{2} m\left(2 g\left(\frac{\sigma}{\rho}-1\right) h\right)$

$\Rightarrow h^{\prime}=\left(\frac{\sigma}{\rho}-1\right) h$