GATE Papers >> Mechanical >> 2017 >> Question No 150

Question No. 150 Mechanical | GATE 2017

A rod of length 20 mm is stretched to make a rod of length 40 mm. Subsequently, it is compressed to make a rod of final length 10 mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is


Answer : (B) -0..69


Solution of Question No 150 of GATE 2017 Mechanical Paper

$ {\mathcal l}_\mathrm i=20\;\mathrm{mm}\;\;\;\;\;\;\;{\mathcal l}_\mathrm f=10\;\mathrm{mm} $

$ \in=\frac{\triangle\mathcal l}{{\mathcal l}_\mathrm i}=\frac{10-20}{20}=-0.5 $

True strain $ \left({\mathrm e}_\mathrm r\right)=\ln\left(1+\in\right)=\ln\left(1-0.5\right)=0.69 $  

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