Constrained, uneven dumbbell

Two beads of mass 2m\displaystyle 2m and m\displaystyle m, connected by a rod of length \displaystyle\ell and of negligible mass, are free to move in a smooth vertical circular wire frame of radius \displaystyle\ell as shown.

Calculate the velocity (in m/s\displaystyle m/s) that should be given to the mass 2m\displaystyle 2m (when the rod is in horizontal position) in counter-clockwise direction so that the rod just becomes vertical.

Details and Assumptions:
\bullet m=250g\displaystyle m = 250g
\bullet =25cm\displaystyle \ell = 25cm
\bullet g=9.8m/s2\displaystyle g = 9.8 m/s^2

Note: This problem appeared in our AITS (All India Test Series) - 6

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