Calculating Max Depth of Apparatus on Mars

[jimbo71]

Homework Statement

On Earth a certain apparatus can safely dive to a depth of 275m in a freshwater lake. This limitation is due to the external gauge pressure on the apparatus. If this device were to be used in a lake on Mars, where the acceleration due to gravity is 3.70m/s^2 but the denisty of water is essentially the same as on earth, the greatest depth to which it could safely dive is closest to
1930m
728m
169m
448m
104m

Homework Equations

p=p0+dgh

The Attempt at a Solution

I calculated the pressure of the Earth dive to be 1.04*10^5pa using p=1.013*10^5+9.81*1*275. I know the g value for Mars will be different and I think the atmospheric pressure on Mars is different but is there a way to calculate the atm pressure of mars? Or am I to solve the problem without using either atmospheric pressures?

 

[LowlyPion]

For this problem you might want to assume that Mars has no atmosphere.

With the lower gravity then the weight of the water will be less by the factor of gravity times the height of the water then won't it? So the maximum on Mars will be G_m*MaxDepth_m = g*275m ?

 

[jimbo71]

ok If I include the atmospheric pressure on Earth and assume Mars has no atmosphere The depth at which the apparatus can dive is much larger than any of the given choices. Am I to calculate the pressure the apparatus can withstand on Earth by not including the atmospheric pressure on earth?

 

[LowlyPion]

I think you can safely assume that the ρgh term will dominate at greater than 100m.

That leaves simply

X = 275 * Ge/Gm

 

[jimbo71]

ok if the pgh term dominates at fairly deep water depths than why would the pressure from water at 100m only add 981 pascals but at sea level the atmospheric pressure is 1.013*10^5. Or are my units wrong?