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GATE 2022 CE (CE2) – Question 52

Engineering Mechanics · Friction and its applications · 2 marks · Numerical answer

A uniform rod KJ of weight w shown in the figure rests against a frictionless vertical wall at the point K and a rough horizontal surface at point J. It is given that w = 10 kN, a = 4 m and b = 3 m. The minimum coefficient of static friction that is required at the point J to hold the rod in equilibrium is ___________. (round off to three decimal places)

Ladder against a smooth vertical wall, with horizontal reach b and vertical height a, resting on rough ground at J. See the attached source image.

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Correct answer: 0.365 to 0.385

Explanation

Taking moments about J eliminates ground forces. The wall reaction R acts at height a, while weight acts at horizontal lever arm b/2: $Ra=wb/2$.

Thus R=10(3)/(2×4)=3.75 kN. Horizontal ground friction equals R and its normal reaction equals w=10 kN. Hence $\mu_{min}=3.75/10=\mathbf{0.375}$.