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

Question No. 150

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

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