Question

A cubical solid aluminium (bulk modulus $=-V \frac{d P}{d V}=70 \,GPa$ ) block has an edge length of $1\, m$ on the surface of the 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 $10 \,ms ^{-2}$, respectively, the change in the edge length of the block in $mm$ is ______

Answer 1

$B = V \frac{dP}{dV}$

Finding the magnitude of the change in the volume:-

70 x 109 =$V \frac{dV}{dx} \times 10^3 \times 10 \times 5 \times 10^3$

7 x 109 = V/dV x 106 x 5

$7000 = \frac{V}{dV} \times 5$

$\frac{dV}{V} = \frac{5}{7000}$

V = l3

$\frac{dV}{V} = 3 \frac{dI}{I}$

$dI = \frac{5}{21000}$

dl = 0.238 mm = 0.24mm