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

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 $α W$ 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?

TestHub · Accepted Answer

∵ Rod is in equilibrium, net torque on the rod about O will be zero. W l 2 + α W l = T 2 l ⇒ W 2 + α W = T 2 ⇒ T = 2 W α + 0 . 5 . . . 1 Now checking options- (A) Force balance on rod, N v + T 2 = W + α W ⇒ N v = W + α W - W 2 + α W ⇒ N v = W 2 Hence, option (A) is correct. (B) Write horizontal force equation, N H = T 2 ⇒ N H = W α + 0 . 5 If α = 0 . 5 , then, N H = W and T = 2 W Hence, option (B) is correct. (D) ∴ Maximum Tension of string = 2 2 W So, to break. T > 2 2 W ⇒ 2 W α + 0 . 5 > 2 2 W ⇒ α > 1 . 5 So, string will break. option (D) correct.

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Options:(select one or more)

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