The marina Trench is located in the pacific ocean, and at one place it is nearly eleven km beneath the surface of water. The water pressure at the bottom of the Trench is about `1.1 xx 10^(8) Pa`. A steel ball of initial volume `0.32 m^(3)` is dropped into the ocean and falls to the bottom of the Trench. what is the change in the volume of the ball when it reaches to the bottom? Bulk modulus for steel =`1.6 xx 10^(11) Nm^(-2)`.

Explanation

Water pressure at the bottom, p `=1.1xx10^(8)` Pa
Initial volume of the steel ball, `V=0.32"m"^(3)`
Bulk modulus of steel, B = `1.6xx10^(11)"Nm"^(-2)`
The ball falls at the bottom of the Pacific Ocean, which is 11 km beneath the surface.
Let the change in the volume of the ball on reaching the bottom of the trench be `DeltaV`.
Bulk modulus, `B=((p)/(DeltaV))/(V)`
`DeltaV=(B)/(pV)`
`=(1.1xx10^(8)xx0.32)/(1.6xx10^(11))`
`=2.2xx10^(-4)"m"^(3)`
Therefore, the change in volume of the ball on reaching the bottom of the trench is `2.2xx10^(-4)"m"^(3)`.