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GATE 2021 CE (CE1) – Question 39

Engineering Mechanics · Friction and its applications · 2 marks · Multiple choice

A weightless wedge of angle 30° raises a weightless block under vertical load Q. The inclined contact has friction coefficient 0.2; all other contacts are frictionless. At impending upward motion, P=aQ. Find a to one decimal.

see the reproduced source diagram and its labels.
  1. 0.6
  2. 0.5
  3. 2.0
  4. 0.9

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Show answer and explanation

Correct answer: (D) 0.9

Explanation

The friction angle satisfies $\tan\phi=0.2$. Force equilibrium for lifting gives $P/Q=\tan(30^\circ+\phi)=(\tan30^\circ+0.2)/(1-0.2\tan30^\circ)=0.87883$. Rounded to one decimal, **a=0.9 (D)**. Friction increases the force above the frictionless value 0.577Q.