One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight αW is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (22)W. Which of the following statement(s) is(are) correct?

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The vertical component of reaction force at O does not depend on α

The horizontal component of reaction force at O is equal to W for α = 0.5

The tension in the rope is 2W for α = 0.5

The rope breaks if α >1.5

answer is A.

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Detailed Solution

T2L=ωL2+αωLT=2ωα+12. For α=12T=ω2T2+RY=ω+αω⇒RY=ω2Rx=T2=ωα+12 For α=12⇒RX=ω For α>1.5⇒T>22ω

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