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A smooth narrow tube in the form of an a...

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.
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Text Solution

Verified by Experts

The correct Answer is:
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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