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 2 W . Which of t

Step-by-step solution

∵ 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) &#8756