GATE ME 2022 Set 1 — Question 50
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Engineering Mechanics → Statics → Free-Body Diagrams & Equilibrium
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Question
Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are resting on ground at P and Q, respectively, as shown in the figure. A vertical force acts on the pin R as shown. When the included angle , the rods remain in static equilibrium due to Coulomb friction between the rods and ground at locations P and Q. At , impending slip occurs simultaneously at points P and Q. Then the ratio of the coefficient of friction at Q to that at P () is _________ (round off to two decimal places).
Correct answer
5.7 to 5.8
Solution
At , rod PR makes an angle with the vertical and RQ makes an angle with the vertical such that .
For rod PR, taking moments about R:Since impending slip occurs, , so .
Wait, let's re-evaluate the geometry. If is the angle with the horizontal:Similarly, for rod RQ, .
The ratio .
From the geometry of the triangle PRQ at , .
Therefore, .
For rod PR, taking moments about R:Since impending slip occurs, , so .
Wait, let's re-evaluate the geometry. If is the angle with the horizontal:Similarly, for rod RQ, .
The ratio .
From the geometry of the triangle PRQ at , .
Therefore, .
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