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GATE 2025 ME – Question 28

Mechanics of Materials · Transformation of stress and strain, Mohr circle · 1 mark · Multiple choice

A metallic square plate is subjected to a uniform hydrostatic pressure ($P$). Choose the correct Mohr's circle representing the state of stress at any point in the plate from the options given below.

For the Mohr's circle, normal stress is positive towards right and shear stress is positive in the upward direction.

Four sketches of the $\sigma$-$\tau$ plane. (A) A single point at $+P$ on the $\sigma$ axis. (B) A single point at $-P$ on the $\sigma$ axis. (C) A circle centred on the origin that passes through $-P$ and $+P$. (D) A circle to the left of the origin that passes through $-P$ and 0.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Show answer and explanation

Correct answer: (B) Option B in the figure

Explanation

Under hydrostatic pressure the normal stress is $-P$ (compressive) in every direction and there is no shear. So every plane has the same stress state, and the Mohr's circle shrinks to a single point at $\sigma = -P$.