Question 424: Properties of Matter

Question

A cubical solid aluminium (bulk modulus = $$ - V{{dP} \over {dV}} = 70GPa$$) 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 10
3
kg m
-3
and 10 ms
-2
, respectively, the change in the edge length of the block in mm is _______.

Accepted Answer

$${{dV} \over V} =  - {{dp} \over B}$$ (where, B = bulk modulus)
$$V = {l^3} \Rightarrow {{\Delta V} \over V} = 3{{\Delta l} \over l}$$
$$3{{\Delta l} \over l} = \left| { - {{\Delta p} \over B}} \right| = {{\rho gh} \over B} \Rightarrow \Delta l = {{\rho ghl} \over {3B}}$$
Substituting the given values, we get $$\Delta$$l = 0.24 mm

Properties of Matter

Integer / Numeric Answer Type