A cabin is moving upwards with a constant acceleration g. A boy standing in the cabin wants to whirl a particle of mass `m` in a vertical circle of radius `l`. (Mass is attached to an ideal string.) Calculate minimum velocity which should be provided at lowermost point (w.r.t cabin) so that particle can just complete the circle.

Explanation

At top most point, `T+2mg=(mv^2)/(r)`
In critical condition, `v^2=2rg`
Applying conservation of energy (or work energy theorem) between top and bottom points.
`1/2mu^2=1/2mv^2+mg2r+mg.2r`
`impliesu^2=v^2+8gr=10gr`
`:. u=sqrt(10gr)`