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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a
The vertical component of reaction force at O does not depend on α
b
The horizontal component of reaction force at O is equal to W for α=0.5
c
The tension in the rope is 2W for α=0.5
d
The rope breaks if α>1.5
answer is A.
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Detailed Solution
T2L=WL2+αWLT=2Wα+12. For α=12T=W2T2+RY=W+αW⇒RY=W2Rx=T2=Wα+12For α=12⇒RX=ωFor α>1.5⇒T>22ω