A smooth narrow tube in the form of an arc AB of a circle of centre O and radius r is fixed so that A is vertically above O and OB is horizontal. Particles P of mass m and Q of mass 2 m with a light inextensible string of length (pi r/2) connecting them are placed inside the tube with P at A and Q at B and released from rest. Assuming the string remains taut during motion, find the speed of particles when P reaches B.
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Explanation

All surface are smooth. Therefore, mechanical energy of the system will remain conserved.
`:.` Decrease in PE of both the blocks
=increase in KE of the blocks
`:. (mgr)+(2mg)((pir)/(2))=(1)/(2)(m+2m)v^(2) " or " v=sqrt((2)/(3)(1+pi)gr)`