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GATE 2016 CE (CE2) – Question 18

Solid Mechanics · Bending moment and shear force in statically determinate beams · 1 mark · Multiple choice

An assembly made of a rigid arm A-B-C hinged at end A and supported by an elastic rope C-D at end C is shown in the figure. The members may be assumed to be weightless and the lengths of the respective members are as shown in the figure. Under the action of a concentrated load P at C as shown, the magnitude of tension developed in the rope is

Diagram for GATE 2016 CE (CE2) question 18
  1. $3P/\sqrt2$
  2. $P/\sqrt2$
  3. $3P/8$
  4. $\sqrt2P$

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Show answer and explanation

Correct answer: (B) $P/\sqrt2$

Explanation

The rope is at45°, so its horizontal and vertical components are each T/sqrt2. Relative to hinge A, C is L to the right and L below, so both components provide counterclockwise moment TL/sqrt2. Balancing their sum against PL gives sqrt2·TL=PL. Therefore **T=P/sqrt2, B**.