Question:
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 $\alpha W$ 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 $(2 \sqrt{2})$ W. Which of the following statement(s) is(are) correct?
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 $\alpha W$ 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 $(2 \sqrt{2})$ W. Which of the following statement(s) is(are) correct?
Updated On: May 22, 2024
- The vertical component of reaction force at $O$ does not depend on $\alpha$
- The horizontal component of reaction force at $O$ is equal to $W$ for $\alpha=0.5$
- The tension in the rope is $2 \,W$ for $\alpha=0.5$
- The rope breaks if $\alpha > 1.5$
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The Correct Option is A, B, D
Solution and Explanation
(A) The vertical component of reaction force at $O$ does not depend on $\alpha$
(B) The horizontal component of reaction force at $O$ is equal to $W$ for $\alpha=0.5$
(D) The rope breaks if \(\alpha\) > 1.5
(B) The horizontal component of reaction force at $O$ is equal to $W$ for $\alpha=0.5$
(D) The rope breaks if \(\alpha\) > 1.5
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