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QJEEAdv20Ph5fd7: JEE Advanced 2020 Physics - Class 11 JEEAdv20Ph5fd7 Solution: A cubical solid aluminium (bulk modulus = ) block has an edge…

A cubical solid aluminium (bulk modulus = −VdPdV=70GPa- V{{dP} \over {dV}} = 70GPa ) 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 _______.

Step-by-Step Verified Solution

dVV=−dpB{{dV} \over V} = - {{dp} \over B} (where, B = bulk modulus)

V=l3⇒ΔVV=3ΔllV = {l^3} \Rightarrow {{\Delta V} \over V} = 3{{\Delta l} \over l}

3Δll=∣−ΔpB∣=ρghB⇒Δl=ρghl3B3{{\Delta l} \over l} = \left| { - {{\Delta p} \over B}} \right| = {{\rho gh} \over B} \Rightarrow \Delta l = {{\rho ghl} \over {3B}}

Substituting the given values, we get Δ\Delta l = 0.24 mm

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