JEE Advanced Physics 2015 Paper 1 #12 (#4) Angular Momentum

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Given: A ring of mass N and radius R is rotating with angular speed omega0 about a fixed vertical axis through its center with 2 point masses m at rest at the center. The 2 masses can move along the 2 mass-less rods with out friction. At an instant omega=(8/9)omega0 and m1, is at (3/5)R from the center.
Find: Where is m2?

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