GATE CE 2022 Set 2 — Question 52
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Structural Engineering → Statics & Rigid Bodies → Equilibrium Equations
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Question
A uniform rod of weight shown in the figure rests against a frictionless vertical wall at the point and a rough horizontal surface at point . It is given that , and .
The minimum coefficient of static friction that is required at the point to hold the rod in equilibrium is ___________. (round off to three decimal places)
Correct answer
0.35 to 0.4
Solution
Let be the horizontal reaction at the frictionless wall , be the vertical reaction at the floor , and be the frictional force at .
.Thus, the required friction force is .
For the rod to be in equilibrium, the friction force must satisfy .
.The minimum coefficient of static friction required is .
1.Vertical equilibrium: .
2.Horizontal equilibrium: .
3.Moment equilibrium about : .
Substituting the given values:.Thus, the required friction force is .
For the rod to be in equilibrium, the friction force must satisfy .
.The minimum coefficient of static friction required is .
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