In July 2015, Oregon State University, the National Oceanic and Atmospheric Administration, and the Coast Guard cooperated to send a hydrophone into Challenger Deep, the deepest part of the Mariana Trench. The titanium shelled recording device withstood the pressure 10,994 meters (nearly 7 miles!) under the ocean's surface. The hydrophone recorded 23 days of audio from the deepest part of the ocean floor. If the spherical hydrophone has a radius of 10 cm, what is the total force exerted on the titanium shell by the ocean water

Explanation:

Pressure due to water column as deep as 10994 meters can be given by the following expression

Pressure = h d g , where h is depth of water , d is density of water and g is acceleration due to gravity .

Pressure = 10994 x 10³ x 9.8

= 10.77 x 10⁷ N / m²

Pressure will act on curved surface of the spherical shell , the effective surface area will be π R² where R is radius of the surface .

Effective surface = 3.14 x 0.1²

= .0314 m²

Total force = pressure due to water column x effective surface

= 10.77 x 10⁷  x .0314 N.

= 33.82 x 10⁵ N .