A soild sphere is initially kept in open air, and the pressure exerted on it by air is `1.0xx10^(5)N//m^(2)` (atmospheric pressure). The sphere is lowered into the ocean to a depth where the pressure is 200 times the atmospheric pressure. The volume of the sphere in air is `0.5 m^(3)`. What is the change in the volume once the sphere is submerged ? Given that bulk modulus is `6.1xx10^(10)N//m^(2)`.

Explanation

What happens when you squeeze a tennis ball in your hand ? Its volume reduces as it shrinks. We can expect same to happen to the sphere when it is subjected to high pressure from the ocean water. We need to perform a simple calculation using Eq. 12-5.
`Delta U=-(V,Delta p)/(B)`.
Substituting the numerical values :
`Delta V=((0.50 m^(3))(2.0xx10^(7)N//m^(2)-1.0xx10^(5)N//m^(2)))/(6.1xx10^(10)N//m^(2))`
`=-1.6xx10^(-4)//m^(3)`.
The negative sign indicates that the volume of the sphere decreases when submerged.