A wire fixed at one end suffers extension when loaded at the other end. The linear strain is 4 x 10-3. The wire also suffers contraction in the radial direction. If the ration of radial strain to linear strain is 0.2. The percentage change in volume is
A) 0.44% B) 0.34 % C) 0.24 % C) 0.14 %
ANS>>>> given is 0.24 % ( C )
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2 Answers
49let D be diiameter and L be the length
\frac{dD}{D}/\frac{dL}{L}=0.2
\frac{dL}{L}=4*10^{-3}
\Rightarrow \frac{dD}{D}=8*10^{-4}
now,\frac{dR}{R}=\frac{dD}{D}=8*10^{-4}
dV=\pi (r-dr)^{2}(l+dl)-\pi r^2l\
ignoring higher powers of dr,
dV=\pi (r^2l+r^2dl+2lrdr+dldr-r^2l)=\pi (r^2dl+ldr) {ignoring drdl as it is very small}
so,\frac{dV}{V}=\frac{\pi (r^2dl+2lrdr)}{\pi r^2l}=\frac{dl}{l}+2\frac{dr}{r}
% change=\frac{dV}{V}*100 { }^0/_{0}
