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Two thin uniform rods of equal length L but made of different materials are joined so that one lies along the x-axis and the other along the y-axis, meeting at the origin. Which of the following can be the position of the centre of mass of the system?

1. (L/3, L/6)
2. (L/2, L/2)
3. (2L/3, L/2)
4. (L/3, L/3)

Correct answer: (L/3, L/6)

Solution

With one rod on the x-axis (COM at (L/2,0)) and one on the y-axis (COM at (0,L/2)), x_cm + y_cm = (L/2)(m1+m2)/(m1+m2) = L/2; only (L/3, L/6) gives this sum.

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