# Tension on string of submerged object.

## Homework Statement

A hollow steel sphere of inner radius 0.9m and outer radius 1m is submeged 1000m below the surface of the sea. Take the density of water to be 1000 kg/m^3 and the density of steel to be 7.8 x 10^3. Calculate the tension in the wire to support the submerged sphere.

B = ρ(f)V(f)g
W = mg

## The Attempt at a Solution

T + B = mg.
Calculate T.
Is this correct? The 1000m below sea level is what's making me doubt myself. Should this be factored into the calculation?

rock.freak667
Homework Helper
Your equation is correct however, I think the 1000 kg/m^3 for water they gave you would be at atmospheric pressure. You might need to get the density at 1000 m. However I don't think the value should vary by too much.

How would you go about calculating the density at a depth of 1000m?

SteamKing
Staff Emeritus
Homework Helper
Water is incompressible. The density of water at sea level is for all intents and purposes the same density at a depth of 1000 m.

haruspex
Homework Helper
Gold Member
2020 Award
According to http://en.wikipedia.org/wiki/Properties_of_water#Compressibility, density increase at 1km due to compression would be only about 0.5%. In practice, higher salinity would be more important. As against that, g would be a tiny bit less. I don't think you're expected to take any of that into account for this question, since it does not specify a salinity or pressure for the given density.

Brilliant. Thanks for that. A little confused as to why the 1000 metres was actually specified so.

haruspex