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GATE 2018 CE (CE1) – Question 38

Engineering Mechanics · System of forces, free-body diagrams, equilibrium equations · 2 marks · Multiple choice

A 250 mm radius, 10 kN cylinder is rolled over a 50 mm obstacle by horizontal centre force P, as shown. All interfaces are frictionless. Minimum P is ______.

Diagram for GATE 2018 CE (CE1) question 38
  1. 4.5 kN
  2. 5.0 kN
  3. 6.0 kN
  4. 7.5 kN

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Show answer and explanation

Correct answer: (D) 7.5 kN

Explanation

At impending lift, take moments about the obstacle corner. P has lever arm $R-h=200$ mm, and W has arm $\sqrt{250^2-200^2}=150$ mm. Thus $P(200)=10(150)$, giving P = 7.5 kN (D).