Pressure - Tension Problem

[kid]

A moored contact mine is an explosive tethered by a cable to the seafloor so that it sits just under the surface of the ocean, then explodes when a ship hits it. Imagine one is a 300 kg sphere with a radius of 0.600 m. If it is 4.00 m below the surface and the tether is low mass enough to be negligible, what is the tension in the tether?

Pbot = ptop + density*g*height
pbot = 101300 + (1030)(9.81)(4)
F/A = 141717.2
F = 141717.2 * pi * .6^2
F = 160197.1N

Is this force the correct force which I am trying to find?

 

[oz93666]

it shouldn't matter whether it's 4 or 400 meters below the surface , the tension will be the same unless density of water changes with depth

you have the radius , so calculate the volume , what is the formula for the volume of a sphere??, then with the density of seawater you can calculate the up force ...

 

[kid]

it shouldn't matter whether it's 4 or 400 meters below the surface , the tension will be the same unless density of water changes with depth

you have the radius , so calculate the volume , what is the formula for the volume of a sphere??, then with the density of seawater you can calculate the up force ...

FBuoyancy = density*volume*g
(1030)(4/3)(pi)(.6)^3(9.81)

Then Fnety = 0 = FBuoyancy - Tension - mg
Could I solve for tension this way?

 

[oz93666]

yes , that's the only way