GATE Papers >> Civil >> 2017 >> Question No 9

Question No. 9 Civil | GATE 2017

A soil sample is subjected to a hydrostatic pressure.$\style{font-family:'Times New Roman'}{\mathrm\sigma}$. The Mohr circle for any point in the soil sample would be


Answer : (C) a point at a distance $\style{font-family:'Times New Roman'}{\mathrm\sigma}$ from the origin


Solution of Question No 9 of GATE 2017 Civil Paper

Radius of Mohr circle $\style{font-family:'Times New Roman'}{=\sqrt{\left(\frac{{\mathrm\sigma}_\mathrm x-{\mathrm\sigma}_\mathrm y}2\right)^2+\mathrm\tau^2}}$

Given : $\style{font-family:'Times New Roman'}{{\mathrm\sigma}_\mathrm x={\mathrm\sigma}_\mathrm y={\mathrm\sigma}_\mathrm z=\mathrm\sigma\;\mathrm\tau=0}$

$\style{font-family:'Times New Roman'}{\mathrm R=\sqrt{\left(\frac{\mathrm\sigma+\mathrm\sigma}2\right)^2+0^2}=0}$

Center $\style{font-family:'Times New Roman'}{=\frac{{\mathrm\sigma}_\mathrm x+{\mathrm\sigma}_\mathrm y}2=\frac{\mathrm\sigma+\mathrm\sigma}2=\mathrm\sigma}$

Mohr circle is a point at a distance of $\style{font-family:'Times New Roman'}{\mathrm\sigma}$ from origin.

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