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?

• 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 $\alpha=0.5$
• C. The tension in the rope is $2 \,W$ for $\alpha=0.5$
• D. The rope breaks if $\alpha > 1.5$

Answer 1

Answer: (A), (B), (D)

The vertical component of reaction force at $O$ does not depend on $\alpha$

Answer 2

(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**