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

Correct Answer: 0.23 - 0.24

\(B = V \frac{dP}{dV}\)

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