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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» 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)`. |
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