GATE CE 2018 Set 1 — Question 38
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Structural Engineering → Statics & Rigid Bodies → Equilibrium Equations
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Question
A cylinder of radius and weight, is rolled up an obstacle of height by applying a horizontal force at its centre as shown in the figure.
All interfaces are assumed frictionless. The minimum value of is
Correct answer
(D) 7.5 kN
Solution
To roll the cylinder over the obstacle, the moment of the applied force about the point of contact with the obstacle (let's call it ) must be greater than or equal to the moment of the weight about the same point.Given:
Radius
Obstacle height
Weight The vertical distance from the center of the cylinder to the point is:
The horizontal distance from the center of the cylinder to the point is:
Taking moments about for the threshold condition:
Thus, the minimum value of required to roll the cylinder up is .
Radius
Obstacle height
Weight The vertical distance from the center of the cylinder to the point is:
The horizontal distance from the center of the cylinder to the point is:
Taking moments about for the threshold condition:
Thus, the minimum value of required to roll the cylinder up is .
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