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 $$_____$$.

Question

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 $$_____$$.

Infinity Learn · Accepted Answer

$$V=a3Differentiating$$,$$dVV=3daaBulk$$ Modulus , $$B=$$−$$VdPdV=$$−$$V($$ρ$$gh)dV=$$−ρ$$gh3daa$$⇒$$70$$×$$109=1$$×$$5000$$×$$103$$×$$10$$×$$13$$×da⇒$$da=$$Δ$$a=521$$×$$10$$−$$3m=0.238mm$$

Elastic behaviour of solids

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Elastic behaviour of solids

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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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