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 ........ $\times 10^{8} \ Nm^{-2}$.

$1\, m^3$ of water is brought inside a lake up to a depth of $200\, m$ from the surface. What will be the change in volume if the bulk modulus of elasticity of water is $22000\, \text{atm}$? (Given: density of water $\rho = 1\times10^3\, kg/m^3$, atmospheric pressure $P_0 = 10^5\, N/m^2$, and $g = 10\, m/s^2$)

The volume contraction of a solid copper cube of edge length $10 \ cm$,when subjected to a hydraulic pressure of $7 \times 10^6 \ Pa$,would be . . . . . . $mm^3$. (Given bulk modulus of copper $= 1.4 \times 10^{11} \ Nm^{-2}$)

$A$ solid sphere of radius $r$ made of a soft material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. $A$ massless piston of area $a$ floats on the surface of the liquid,covering the entire cross-section of the cylindrical container. When a mass $m$ is placed on the surface of the piston to compress the liquid,the fractional decrement in the radius of the sphere,$\left( \frac{dr}{r} \right)$ is:

The density $\rho$ of water of bulk modulus $B$ at a depth $y$ in the ocean is related to the density at the surface $\rho_0$ by the relation:

Explain hydraulic stress,volume stress and volume strain.