GATE CE 2022 Set 1 — Question 46
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Structural Engineering → Statics & Rigid Bodies → Equilibrium Equations
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Question
A horizontal force of kN is applied to a homogeneous body of weight 25 kN, as shown in the figure. The coefficient of friction between the body and the floor is 0.3. Which of the following statement(s) is/are correct?
- A.The motion of the body will occur by overturning.
- B.Sliding of the body never occurs.
- C.No motion occurs for kN.
- D.The motion of the body will occur by sliding only.
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Correct answer
(A) The motion of the body will occur by overturning.; (C OR A); (B) Sliding of the body never occurs.; (C) No motion occurs for P ≤ 6 kN.
Solution
To determine the mode of motion, we compare the force required for sliding () and overturning ().
1.Sliding condition: kN.
2.Overturning condition: Taking moments about the bottom-left corner (the potential point of rotation), the overturning moment must exceed the restoring moment: kN.
Since , the body will start to overturn at kN before it can slide. - Statement (A) is correct: Motion occurs by overturning.
- Statement (C) is correct: Since motion starts at 6.25 kN, no motion occurs for kN.
- Statement (B) is incorrect: Sliding can occur if overturning is prevented.
- Statement (D) is incorrect: Overturning precedes sliding.
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