$A$ 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 compressibility of water is $4 \times 10^{-5}$ per unit atmospheric pressure. The decrease in volume of $100 \ cm^3$ of water under a pressure of $100 \ atm$ will be ......... $cm^3$.

What is compressibility? Give its unit and dimensional formula.

Which of the following moduli of elasticity is possible in solids,liquids,and gases?

Consider a fluid in a container. Let the density of the fluid at the surface and at depth $H$ be $\rho_0$ and $\rho$ respectively. The bulk modulus of the fluid is $B_0$. If $\rho = \frac{\rho_0}{1 - \frac{\rho g H}{B_0}}$, find the constant $\alpha$ in the expression $\rho = \frac{\rho_0}{1 + \alpha \rho g H}$ (Assume $\frac{\rho - \rho_0}{\rho_0} \ll 1$).

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