A particle of mass m is attached to the end of a light inextensible string of length 2a, the other end of which is attached to a fixed-point P. The particle is projected horizontally from the point 2a below P with speed v. As it comes in level with P, a peg distant a from P catches the string. In the subsequent motion, the particle can just describe a full circle about Q. Find v. (see figure).
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