How much pressure (in atm) is needed to compress a sample of water by $0.4 \%$ (in $\text{ atm}$)? (Assume,Bulk modulus of water $\approx 2.0 \times 10^9 \text{ Pa}$)

If the average depth of an ocean is $4000 \ m$ and the bulk modulus of water is $2 \times 10^9 \ N m^{-2}$,then the fractional compression $\frac{\Delta V}{V}$ of water at the bottom of the ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is . . . . . . (Given,$g=10 \ m s^{-2}, \rho=1000 \ kg m^{-3}$)

The average density of Earth's crust $10 \ km$ beneath the surface is $2.7 \ g/cm^3$. The speed of longitudinal seismic waves at that depth is $5.4 \ km/s$. The bulk modulus of Earth's crust,considering its behavior as a fluid at that depth,is:

$A$ bottle has an opening of radius $a$ and length $b$. $A$ cork of length $b$ and radius $(a + \Delta a)$,where $(\Delta a << a)$,is compressed to fit into the opening completely (see figure). If the bulk modulus of the cork is $B$ and the frictional coefficient between the bottle and the cork is $\mu$,then the force needed to push the cork into the bottle is:

$A$ 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,$B = 8 \times 10^{10} \; Pa$)

$A$ ball is taken to a depth of $200 \ m$ in a lake. The decrease in its volume is $0.1\%$. Calculate the bulk modulus of the material of the ball.