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GATE 2022 CE (CE1) – Question 46

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

A horizontal force of P 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?

Rectangular block with weight 25 kN, width 1 m and applied horizontal force P at height 2 m. See the attached source image.
  1. The motion of the body will occur by overturning.
  2. Sliding of the body never occurs.
  3. No motion occurs for P ≤ 6 kN.
  4. The motion of the body will occur by sliding only.

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Show answer and explanation

Correct answer: (A) The motion of the body will occur by overturning.; (B) Sliding of the body never occurs.; (C) No motion occurs for P ≤ 6 kN.

Explanation

The sliding threshold is $P_s=\mu W=0.3(25)=7.5$ kN. Taking moments about the leading bottom corner, overturning begins when $P(2)=25(0.5)$, giving $P_t=6.25$ kN.

Since tipping occurs before sliding, the initial motion is overturning, and no motion occurs for P≤6 kN. Thus **A, B and C** apply to the onset-of-motion model; D is false.