The compressibility of water is $6 \times 10^{-10} \,m^{2}/N$. If one litre of water is subjected to a pressure of $4 \times 10^{7} \,N/m^{2}$, then the decrease in its volume in millilitre will be

When a rubber ball is taken to a depth of $h$ meters in deep sea,its volume decreases by $0.5\, \%$. Calculate the depth $h$. (Given: Bulk modulus of rubber $B = 9.8 \times 10^{8} \, \text{N/m}^2$,Density of sea water $\rho = 10^{3} \, \text{kg/m}^3$,$g = 9.8 \, \text{m/s}^2$)

The average density of Earth's crust $10 \ km$ beneath the surface is $2.7 \ g/cm^3$. The speed of longitudinal seismic waves at that depth is $5.4 \ km/s$. The bulk modulus of Earth's crust,considering its behavior as a fluid at that depth,is:

The density of a metal at normal pressure is $\rho$. Its density when it is subjected to an excess pressure $p$ is $\rho^{\prime}$. If $B$ is the Bulk modulus of the metal,the ratio $\frac{\rho^{\prime}}{\rho}$ is:

$A$ uniform cube is subjected to volume compression. If each side is decreased by $1\%$,then the bulk strain is

$A$ 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: