A solid copper cylinder of length L = 0.65m is placed on a horizontal surface and subjected to a vertical compressive force F=1000Ndirected down-ward and distributed uniformly over the end face. What will be the resulting change in volume of the cylinder if Young.s modulus of copper is 1.3xx10^(11)Nm^(2) and Poissons ratio sigma=0.34

A solid copper cylinder of length L = 0.65m is placed on a horizontal

1.	A solid copper cylinder of length L = 0.65m is placed on a horizontal surface and subjected to a vertical compressive force F=1000Ndirected down-ward and distributed uniformly over the end face. What will be the resulting change in volume of the cylinder if Young.s modulus of copper is 1.3xx10^(11)Nm^(2) and Poissons ratio sigma=0.34
Answer» Solution :`sigma=(-(dr)/(r))/((DL)/(L)) (dr)/(r)=-(sigmadl)/(l) , V= pi r^(2)L, (DV)/(V)=(2dr)/(r)+(dL)/(L) RARR (dV)/(V)=-2 sigma (dL)/(L)+(dL)/(L)` `(dV)/(V)=(dL)/(L)[1-2sigma] rArr dV=V(dL)/(L) [1-2sigma],dV= PIR^(2)L "strin" [1-2sigma] , dV=A.L.F//AY[1-2 sigma]` `dV=(FL)/(Y)[1-2sigma], dV=(100xx0.65)/(1.3xx10^(11))[1-2xx0.34]=1.6xx10^(-9)m^(3) rArr dV=1.6 mm^(3)`