$A$ solid cube of copper of edge $10 \, cm$ is subjected to a hydraulic pressure of $7 \times 10^6 \, Pa$. If the Bulk modulus of copper is $140 \, GPa$,then the contraction in its volume will be ................ $m^3$.

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 pressure required to decrease the volume of $4000 \ cc$ water by $0.05 \%$ is (Bulk modulus of water $= 2.2 \times 10^9 \ N/m^2$)

Bulk modulus of water is $2 \times 10^9 \ N/m^2$. The pressure required to increase the volume of water by $0.1 \%$ in $N/m^2$ is:

The compressibility of water is $5 \times 10^{-10} \ m^2/N$. $A$ pressure of $15 \times 10^6 \ Pa$ is applied on $100 \ ml$ volume of water. The change in the volume of water is:

An external pressure $P$ is applied on a cube at $0^o C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by