A cubical solid aluminium (bulk modulus $=-V \frac{ dP }{ dV }=70 GPa$ ) 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 . . . . .
IIT 2020, Easy
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$\frac{d V}{V}=\frac{3 d a}{a}$
$B=-V \frac{d P}{d V}=\frac{-V(\rho g h)}{d V}=\frac{-\rho g h}{3 da } a$
$70 \times 10^9=\frac{1 \times 5000 \times 10^3 \times 10 \times 1}{3 \times da }$
$da =\Delta a =\frac{5}{21} \times 10^{-2} m =2.38 mm$
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