Derive expression for linear velocity at lowest point,midway point and top point for a particle revolving in a verticle circle - Physics -

Question

Derive expression for linear velocity at lowest point,midway point
and top point for a particle revolving in a verticle circle if it
has to jump complete circular motion without string slacking at top

Vara · Accepted Answer

Dear
Student,
Please find below the solution
to the asked query:
At the highest position:Tension=0T=mv2r-mg0=mv2r-mgmv2r=mgv=rgAt the lowest position:Total energy at the lowest position=Total energy at the highest position12mv12=mgh+12mv2mv12=2mgh+mv2v12=2gh+v2v12=2gh+v2      =2g2r+rg       =5rgv1=5rgAt the midpoint:Total energy at the lowest position=Total energy at the mid position12mv12=mgh+12mv2mv12=2mgh+mv2v12=2gh+v2v12=2gh+v2      =2gr+rg       =3rgv1=3rg
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clear your doubts about Circular
motion
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Derive expression for linear velocity at lowest point,midway point and top point for a particle revolving in a verticle circle if it has to jump complete circular motion without string slacking at top.