GATE ME 2014 Set 4 — Question 47
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Engineering Mechanics → Statics → Free-Body Diagrams & Equilibrium
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Question
A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the axis, stands on a rough level floor as shown in the figure. A force is applied at mid-height on the wardrobe so as to tip it about point without slipping. What are the minimum values of the force (in newton) and the static coefficient of friction between the floor and the wardrobe, respectively?
Correct answer
(A) 490.5 and 0.5
Solution
1.Calculate the weight of the wardrobe: N.
2.To tip the wardrobe about point , the moment due to force must balance the restoring moment due to weight . Taking moments about :
where m (mid-height) and m (width).3.To tip without slipping, the friction force must be at least equal to . The maximum static friction is .
4.The minimum values are N and .
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