A small bob \( A \) of mass \( m \) is attached to a massless rigid rod of length \( 1 \, \text{m} \) pivoted at point \( P \) and kept at an angle of \( 60^\circ \) with vertical as shown in figure. At distance of \( 1 \, \text{m} \) below point \( P \), an identical bob \( B \) is kept at rest on a smooth horizontal surface that extends to a circular track of radius \( R \) as shown in figure. If bob \( B \) just manages to complete the circular path of radius \( R \) upto a point \( Q \) after being hit elastically by bob \( A \), then radius \( R \) is ______ \( \text{m} \).
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