Q21 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 $1.1 \times 10 ^ 8 Pa$ 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?

The pressure at the bottom of the trench, $P=1.1\times 10^{8}Pa$

The initial volume of the steel ball, V = 0.32 m

Bulk Modulus of steel, $B=1.6\times 10^{11}Nm^{-2}$

$\\B=\frac{P}{\frac{\Delta V}{V}}\\ \Delta V=\frac{PV}{B}\\ \Delta V=\frac{1.1\times 10^{8}\times 0.32}{1.6\times 10^{11}}\\ \Delta V=2.2\times 10^{-4}m^{3}$

The change in the volume of the ball when it reaches the bottom of the trench is  $2.2\times 10^{-4}m^{3}$.

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