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GATE 2021 AG – Question 37

Soil and Water Conservation Engineering · Soil Mechanics · 2 marks · Multiple choice

An annular soil-shear device has inner/outer diameters240/300 mm. Soil failure torque50 N m. Find soil shear strength in kPa. Use π=3.14.

  1. 14.49
  2. 18.94
  3. 21.54
  4. 28.98

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Correct answer: (A) 14.49

Explanation

For uniform shear stress τ on the annulus,$T=\int\tau r\,dA=2\pi\tau(R_o^3-R_i^3)/3$. Hence $\tau=3(50)/[2(3.14)(.15^3-.12^3)]=14.50$ kPa, matching **14.49,A** within source rounding. The radii, not diameters, enter the cubic formula.

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