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JEE MainPhysicsCenter of Mass, Momentum and Collision

A uniform wire is bent at a right angle at the origin such that its two segments lie along the positive x-axis and positive y-axis. If the y-coordinate of the centre of mass of this wire is exactly three times its x-coordinate, what is the ratio of the length of the segment along the y-axis to the length of the segment along the x-axis?

Options

  1. A3
  2. B1 3
  3. C1 3
  4. D3

Correct answer

D. 3

Step-by-step solution

Let the length of the segment along the x-axis be L_x and the length of the segment along the y-axis be L_y . Since the wire is uniform, the mass of each segment is proportional to its length. Let the linear mass density be . Mass of the x-segment, m_x = L_x Mass of the y-segment, m_y = L_y The centre of mass of the x-segment is at ( L_x 2 , 0 ) and the centre of mass of the y-segment is at (0, L_y 2 ) . The x-coordinate of the centre of mass of the entire wire is: x_ cm = m_x ( L_x 2 ) + m_y (0) m_x + m_y = L_x^2

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