Q.

A cubical solid aluminium (bulk modulus =−VdPdV=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 103 kg m−3 and 10 ms−2, respectively, the change in the edge length of the block in mm is _____.

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answer is 0.24.

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Detailed Solution

V=a3Differentiating,dVV=3daaBulk Modulus , B=−VdPdV=−V(ρgh)dV=−ρgh3daa⇒70×109=1×5000×103×10×13×da⇒da=Δa=521×10−3m=0.238mm
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A cubical solid aluminium (bulk modulus =−VdPdV=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 103 kg m−3 and 10 ms−2, respectively, the change in the edge length of the block in mm is _____.