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Most Important Selected Qs for JEE AdvancedPhysicsCenter of Mass, Momentum and Collision

Paragraph: A 'U' shaped uniform rod of each of side having length ' ' and mass ' m ' is hinged from the one end of one of its limbs as shown. Question: If the system is displace by small angle then time period of oscillation is

Options

  1. A3 5 g
  2. B2 6 5 g
  3. C6 5 g
  4. D2 3 5 g

Correct answer

B. 2 6 5 g

Step-by-step solution

Let the point of suspension is origin(O), then C.M. lies on vertical line when it is in equilibrium position. aligned & x _ cm = m (0)+ m ( L / 2)+ m ( L ) 3 ~m = L / 2 and & y _ cm = m (- L / 2)+ m (- L )+ m (- L / 2) 3 ~m = -2 ~L 3 & = L / 2 2 ~L / 3 =3 / 4 = ⁻¹(3 / 4) or 37^0 & ~d ^2= ( 2 ~L 3 )^2+ ( L 2 )^2 & ~d = 5 ~L 6 aligned Moment of inertia I = Mk ^2=4 ~m ( ^2 12 + ^2 4 + ^2 2 )- m ^2 3 =3 ~m ^2 (Assume full square and calculate moment of inertia about origin and subtract the moment of inertia of fourth r

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