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.

The increase in the pressure required to decrease the volume $(\Delta V)$ of water is $6.3 \times 10^7 \text{ N/m}^2$. The percentage decrease in the volume is . . . . . . . (Bulk modulus of water = $2.1 \times 10^9 \text{ N/m}^2$.) (in $\%$)

The fractional compression $\left(\frac{\Delta V}{V}\right)$ of water at a depth of $2.5 \ km$ below the sea level is . . . . . . $\%$. Given: the Bulk modulus of water $B = 2 \times 10^9 \ N m^{-2}$,density of water $\rho = 10^3 \ kg m^{-3}$,and acceleration due to gravity $g = 10 \ m s^{-2}$.

An increase in pressure required to decrease the $200 \ L$ volume of a liquid by $0.004\%$ in a container is .......... $kPa$ (Bulk modulus of the liquid $= 2100 \ MPa$).

Find the stress developed inside a tooth cavity filled with copper when hot tea at a temperature of $57^{\circ} C$ is drunk. You can take the body (tooth) temperature to be $37^{\circ} C$ and $\alpha = 1.7 \times 10^{-5} {}^{\circ} C^{-1}$,bulk modulus for copper $B = 140 \times 10^9 \ Nm^{-2}$.

$A$ spherical ball contracts in volume by $0.02 \%$,when subjected to a normal uniform pressure of $50$ atmosphere. The Bulk modulus of its material is ............. $Nm^{-2}$.