GATE CE 2021 Set 1 — Question 39
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Structural Engineering → Statics & Rigid Bodies → Equilibrium Equations
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Question
A wedge M and a block N are subjected to forces P and Q as shown in the figure. If force P is sufficiently large, then the block N can be raised. The weights of the wedge and the block are negligible compared to the forces P and Q. The coefficient of friction () along the inclined surface between the wedge and the block is . All other surfaces are frictionless. The wedge angle is .
The limiting force P, in terms of Q, required for impending motion of block N to just move it in the upward direction is given as . The value of the coefficient '' (round off to one decimal place) is
Correct answer
(D) 0.9
Solution
Let be the normal reaction at the inclined interface (Surface 2) and be the friction force. For impending upward motion of block N, friction acts downwards along the incline on N.For block N (equilibrium in vertical direction):
For wedge M (equilibrium in horizontal direction):
Thus, .
For wedge M (equilibrium in horizontal direction):
Thus, .
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