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JEE MainPhysicsCenter of Mass, Momentum and Collision

A uniform L-shaped rigid rod has two straight arms of lengths 40 cm and 30 cm . It is suspended freely from a pivot at the right-angled corner and allowed to come to equilibrium. The value of , where is the angle made by the 40 cm arm with the vertical, is:

Options

  1. A9 16
  2. B3 4
  3. C4 3
  4. D16 9

Correct answer

A. 9 16

Step-by-step solution

Let the right-angled corner be at the origin (0,0) . Assume the 40 cm arm lies along the positive x-axis and the 30 cm arm lies along the positive y-axis. Since the rod is uniform, the mass of each arm is proportional to its length. Let the linear mass density be . Mass of the 40 cm arm, m₁ = 40 Mass of the 30 cm arm, m₂ = 30 The centre of mass of the 40 cm arm is at (20, 0) and the centre of mass of the 30 cm arm is at (0, 15) . The coordinates of the centre of mass of the entire rod are: x_ cm = m₁(20) + m₂(0) m₁

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