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 ______
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 ______
Updated On: Apr 25, 2024
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Correct Answer: 0.23 - 0.24
Solution and Explanation
\(B = V \frac{dP}{dV}\)
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
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