Q: A cubical solid aluminium (bulk modulus = -VdP/dV = 70 GPa) block has an edge length 1 m on the surface of earth . It is kept on the floor of a 5 km deep ocean . Taking the average density of water and the acceleration due to gravity to be 10^{3} kg/m^3 and 10 m/s^2 respectively , the change in edge length of the block in mm is …..

Ans: (0.24)

Solution: $\displaystyle \frac{\Delta V}{V} = -\frac{\Delta p}{B}$ ; Where B = Bulk modulus

V = l^{3}

$\frac{\Delta V}{V} = 3 \frac{\Delta l}{l}$

$\displaystyle 3\frac{\Delta l}{l} = |-\frac{\Delta p}{B}|=\frac{\rho g h}{B} $

$\displaystyle \Delta l = \frac{\rho g h l}{3 B} $