The compressibility of water per unit atmospheric pressure is $\sigma$. If there is a decrease in volume $V$ due to an applied pressure $P$,find the change in volume.

$A$ spherical ball of volume $2000 \text{ cm}^3$ is subjected to a hydraulic pressure of $15 \text{ atm}$. If the change in volume is $5 \times 10^{-2} \text{ cm}^3$,the bulk modulus of the material of the spherical ball is (Given: $1 \text{ atm} = 10^5 \text{ Nm}^{-2}$)

The volume of a material reduces by $2 \%$ when the pressure is increased from $1 \text{ atm}$ to $2 \text{ atm}$. What is its bulk modulus?

Bulk modulus of water is $2 \times 10^9 \ N/m^2$. The pressure required to increase the volume of water by $0.1 \%$ in $N/m^2$ is:

$A$ rubber ball is taken into the deep sea such that its volume decreases by $x \%$. The bulk modulus of rubber is $K$ and the density of sea water is $\rho$. The depth $h$ to which the rubber ball is taken is proportional to $(g = \text{acceleration due to gravity})$:

$A$ swimming pool has a depth of $22 \ m$ and area $700 \ m^2$. Calculate the fractional change $\frac{\Delta V}{V}$ of water at the bottom of the swimming pool. Given that the bulk modulus of water is $2.2 \times 10^9 \ N \ m^{-2}$,$g = 10 \ m \ s^{-2}$,and the density of water is $1000 \ kg \ m^{-3}$.