$A$ liquid of bulk modulus $k$ is compressed by applying an external pressure such that its density increases by $0.01 \%$. The pressure applied on the liquid is

What is the relationship between the isothermal bulk modulus $E_\theta$ and the adiabatic bulk modulus $E_\phi$? (where $\gamma = C_p/C_v$)

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 $= 2100 \ MPa$).

The average depth of the Indian Ocean is about $3000 \,m$. The value of fractional compression $\left(\frac{\Delta V}{V}\right)$ of water at the bottom of the ocean is (given that the bulk modulus of water is $2.2 \times 10^9 \,N/m^2$,$g = 9.8 \,m/s^2$,$\rho_{H_2O} = 1000 \,kg/m^3$):

$A$ 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:

The bulk modulus of a liquid is $3 \times 10^{10} \ Nm^{-2}$. The pressure required to reduce the volume of liquid by $2 \%$ is ........ $\times 10^{8} \ Nm^{-2}$.