Question

A cube is subjected to pressure of `5 xx 10^(5)N//m^(2)`. Each side of the cube is shortened by 1%. Find volumetric strain and bulk modulus of elasticity of cube.

Answer 1

Let l be the initial length of each side of cube.
Final length = `(1-(1)/(100)l)=99/100 l`
Initial volume `V_(i)=t^(3)`
Final volume , `V_(f)=((99)/(100)l)^(3)-l^(3)`
Volumetric strain = `(Delta V)=V_(f)-V_(i)`
`=(1-1/100)^(3) -1 = -3/100 = -0.03`
Normal stress=increase in pressure
`=5 xx 10^(5) N//m^(2)`
`:.` Bulk modulus of elasticity , `B=(5 xx 10^(5))/(-0.03)`
`=1.67 xx 10^(7)N//m^(2)`.