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JEE Advanced Physics Laws of Motion 2021 JEE Advanced 2021 (Paper 2)

JEE Advanced Physics Question (2021) — Solution

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 2 W . Which of the following statement(s) is(are) correct?  

Options

  1. A. The vertical component of reaction force at  O  does not depend on  α .
  2. B. The horizontal component of reaction force at  O  is equal to  W  for  α = 0 . 5 .
  3. C. The tension in the rope is  2 W  for  α = 0 . 5 .
  4. D. The rope breaks if  α > 1 . 5 .

Answer

D. The rope breaks if  α > 1 . 5 .

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)  ∴  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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