The average depth of an oil well is $2000 \, m$. If the bulk modulus of oil is $8 \times 10^8 \, N/m^2$ and the density of oil is $1500 \, kg/m^3$, the fractional compression at the bottom of the well is (take $g = 10 \, m/s^2$): (in $\%$)

$A$ cube of metal is subjected to a hydrostatic pressure of $4 \; GPa$. The percentage change in the length of the side of the cube is close to $.......\%$. (Given bulk modulus of metal,$B = 8 \times 10^{10} \; Pa$)

How many times more compressible are gases compared to solids?

The bulk modulus of rubber is $9.1 \times 10^8 \, N/m^2$. To what depth should a rubber ball be taken in a lake so that its volume is decreased by $0.1\%$? (Take density of water $\rho = 10^3 \, kg/m^3$ and $g = 10 \, m/s^2$)

The Mariana Trench is located in the Pacific Ocean,and at one place it is nearly $11 \; km$ beneath the surface of the 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 the bottom? (Bulk modulus of steel $B = 1.6 \times 10^{11} \; N/m^{2}$)

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 $B = 140 \times 10^9 \ Nm^{-2}$.