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A particle of mass m is attached to one ...

A particle of mass m is attached to one end of a weightless and inextensible string of length L. The particle is on a smooth horizontal table. The string passes through a hole in the table and to its other and is attached a small particle of equal mass m. The system is set in motion with the first particle describing a circle on the table with constant angular velocity `omega_(1)` and the second particle moving in the horizontal circle as a conical pendulum with constant angular velocity `omega_(2)` Show that the length of the portions of the string on either side of the hole are in the ratio `omega_(2)^(2): omega_(1)^(2)`

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