Answer
(a) The gauge pressure is $1.86\times 10^6~Pa$
(b) In the earth's ocean, we can find this gauge pressure at a depth of 184 meters.
Work Step by Step
(a) We can find the gauge pressure at a depth of 500 meters.
$P_G = \rho~g_{Mars}~h$
$P_G = (1000~kg/m^3)(3.71~m/s^2)(500~m)$
$P_G = 1.86\times 10^6~Pa$
(b) We can find the depth $h$ below the surface in the earth's ocean which has this gauge pressure.
$\rho~g~h = P_G$
$h = \frac{P_G}{\rho~g}$
$h = \frac{1.86\times 10^6~N/m^2}{(1030~kg/m^3)(9.80~m/s^2)}$
$h = 184~m$
In the earth's ocean, we can find this gauge pressure at a depth of 184 meters.
