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 rube 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. .

A smooth narrow tube in the form of an arc AB of a circle of centre O

1.	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 rube 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. .
Answer» Correct Answer - A::B::C All surfaces are smooth. Therefore, mechanical energy of the system will remain conserved. `:.` Decrease in PE of both the blocks =increase in KE of both blocks `:. (mgr)+(2mg)(pir/2)=1/2(m+2m)v^(2)` or `v =sqrt((2)/(3)(1+pi)gr)`.

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