A particle of mass m is tied to an inextensible massless string of length l whose other end is fixed, is projected vertically up with a velocity u0=√kgl at t=0 such that string being just taut and making an angle 60° with lower vertical at the instant of projection.
For the string-particle system to complete vertical circle,range k is best described as??
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UP 0 DOWN 0 0 2
2 Answers
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Now Lcos60° + h = L
=> h = L(1 - cos60°)
=> h = L2
I have taken the reference point to be the lowermost point for convenience.
Now if the particle can reach the topmost point, from there it will be able to complete the vertical circle on the action of gravity(correct me if wrong).
Let the topmost point be C.
Energy at B = Energy at critical point C(Tension = 0 at this critical point)
mu022 + mgL2 = 2mgL + 0
=> kmgL + mgL = 4mgL
=> k = 3
So k ≥ 3 for completion of vertical circle.
