The isothermal bulk modulus of a gas at atmospheric pressure is:

$A$ 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 ............... $N / m^2$.

$A$ 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 $(g = \text{acceleration due to gravity})$:

$A$ solid sphere of radius $10\,cm$ is subjected to a pressure of $5\times 10^8\,Nm^{-2}$. Determine the change in its volume. The bulk modulus of the material of the sphere is $3.14 \times 10^{11}\,Nm^{-2}$.

$A$ ball falling in a lake of depth $200 \ m$ shows $0.1\%$ decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

The adiabatic bulk modulus of a gas at a pressure $P$ is (where $\gamma$ is the ratio of specific heat capacities of the gas).